SlideShare ist ein Scribd-Unternehmen logo
1 von 38
• 5x
• 2x – 3
• 3x + y
• 2xy + 5
• xyz + x + y + z
• x2 + 1
• y + y2
Some examples of expressions
Algebraic Expressions
• 5x = 25
• 2x – 3 = 9
• 2y +
𝟓
𝟐
= 8
• 6z + 10 = -7
• 9x – 11 = 8
Some examples of equations
Equations use the equality (=) sign
If yes = equation 
If no = equation 
These are linear expressions:
• 2x
• 2x + 1
• 3y – 7
• 12 – 5z
These are not linear expressions
• 𝑥2
+ 1
• y+𝑦2
• 1+z+𝑧2
+𝑧3
(since highest
power of
variable > 1)
A linear expression is an
expression whose
highest power of the
variable is one only.
Linear Equations
The equation of a straight line is the linear equation. It could be in one
variable or two variables.
Linear Equation in One Variable
If there is only one variable in the equation then it is called a linear
equation in one variable.
The general form is
ax + b = c, where a, b and c are real numbers and a ≠ 0.
Example
x + 5 = 10
y – 3 = 19
These are called linear equations in one variable
because the highest degree of the variable is one and
there is only one variable.
• We assume that the two
sides of the equation are
balanced.
• We perform the same
mathematical operations on
both sides of the equation,
so that the balance is not
disturbed.
How to find the solution of an equation?
X + 3 = 7
X = 7
The value which when substituted for the
variable in the equation, makes its two
sides equal, is called a solution ( or root )
of the equation.
REMEMBER
• The same number can be added to both the sides of the
equation.
• The same number can be subtracted from both the sides of
the equation.
• We can multiply or divide both the sides of the equation by
the same non-zero number.
https://www.liveworksheets
.com/ng1353447tn
• Solve the linear equation: 4x + 3 = 15 – 2x
Solution: 4x + 3 = 15 – 2x
On subtracting 3 from both the sides, we get
4x + 3 – 3 = 15 – 2x – 3
Or,
4x = 12 – 2x
4x + 2x = 12 – 2x + 2x
6x = 12
𝟔𝒙
𝟔
=
𝟏𝟐
𝟔
X = 2
Hence, x = 2 is the solution of the given solution.
MATHEMATICS – I
CHAPTER – 1
LINEAR EUATIONS IN TWO
VARIABLES
CLASS X
• ax + b = c, where a, b and c are real numbers and
a ≠ 0.
Example ,
2x + 3 = 6
• ax + by + c = 0, where a, b and are real numbers,
such that a ≠ 0, b ≠ 0.
Example,
2x + 5y + 8 = 0
Linear equation in one variable
Linear equation in two variable
ax + by + c = 0, where a, b and c are
real numbers, such that a ≠ 0, b ≠ 0.
Example:
a) 4x + 3y = 4
b) -3x + 7 = 5y
c) X = 4y
d) Y = 2 – 3x
• Compare the equation ax + by + c = 0 with
equation 2x + 3y = 4.37 and find the values of a,
b and c?
a)a = 2, b = 3 and c = 4.37
b)a = 2, b = 3 and c = - 4.37
c)a = 2, b = -3 and c = - 4.37
d)a = -2, b = 3 and c = 4.37
Solution: b) a = 2, b = 3 and c = - 4.37
ax + by + c = 0
2x + 3y + (-4.37) = 0
Solution of a linear equations in two variable
The solution of a linear equation in two variables is an
ordered pair of numbers, which satisfies the equation.
The values x = m and y = n are said to be the solution of
the linear equation.
‘ax + by + c = 0’ if
am + bn + c = 0
• Show that x = 4 and y = -1 satisfy the equation x + 3y –
1 = 0
Solution:
On substituting x = 4 and y = -1 in equation x + 3y – 1 = 0,
we get
L. H. S = 4 + 3 X (-1) – 1
= 4 – 3 – 1
= 0
= R. H. S
Hence, x = 4 and y = -1 satisfy the equation x + 3y – 1 = 0.
Oranges + Apples = 10
Oranges Apples Fruits
1 9 10
2 8 10
3 7 10
4 6 10
5 5 10
6 4 10
7 3 10
8 2 10
9 1 10
Hit and Trial Method
Hint –
Apples are 2 more than oranges
6 Apples + 4 Oranges = 10
6 Apples – 4 Oranges = 2
x + y = 10
x – y = 2
(2 – Equations, 2 – Variables or 2 – Unknowns)
This pair of equation is called linear of equation in two
variables or
System of equation or simultaneous equations.
Algebraic or Graphical Method.
• If x = 1, y = 2 is a solution of the equation 3x + 2y = k,
then the value of k is
a) 7
b) 6
c) 5
d) 4
Solution: 3x + 2y = k
3 (1) + 2 (2) = k
3 + 4 = k
K = 7
• 𝑻𝒉𝒆 𝒄𝒐𝒎𝒎𝒐𝒏 𝒔𝒐𝒍𝒖𝒕𝒊𝒐𝒏 𝒐𝒇 𝟑𝒙 + 𝟐𝒚 = 𝟔 𝒂𝒏𝒅 𝟓𝒙 − 𝟐𝒚 = 𝟏𝟎 𝒊𝒔
a)(0,3)
b)(0,-5)
c)(2,0)
d)(1,0)
Solution:
3x + 2y = 6
5x – 2y = 10
+
-------------------------------
8 x + 0 = 16
x =
𝟏𝟔
𝟖
= 2
3x + 2y = 6
3 (2) + 2y = 6
6 + 2y = 6
2y = 6 – 6
2y = 0
Y = 0
(x, y) = (2,0)
• Solution of the linear equation (x-1) = (
𝟑
𝟒
)(x+1) – (
𝟏
𝟐
) will be
a) x = 5
b)x = 4
c) x = 3
d)x = 1
Solution: (x-1) = (
𝟑
𝟒
)(x+1) – (
𝟏
𝟐
)
x – 1 =
𝟑
𝟒
x +
𝟑
𝟒
-
𝟏
𝟐
x -
𝟑
𝟒
x =
𝟑
𝟒
-
𝟏
𝟐
+ 1
𝒙(𝟒−𝟑)
𝟒
=
(𝟔−𝟒)
𝟖
+ 1
𝒙
𝟒
=
𝟐
𝟖
+ 1
2x = 2 + 8
2x = 10
X = 5
• What is the value of x in the equation 𝟑 x – 2 = 2 𝟑 + 4
a) 2 ( 1 - 𝟑 )
b) 2 ( 1 + 𝟑 )
c) 1 + 𝟑
d) 1 - 𝟑
Solution – 𝟑 x – 2 = 2 𝟑 + 4
• 𝟑 x = 2 𝟑 + 4 + 2
• 𝟑 x = 2 𝟑 + 6
•
𝟑
𝟑
x =
𝟐 𝟑+ 𝟔
𝟑
• x = 2 +
𝟔
𝟑
• x = 2 + (
𝟔
𝟑
x
𝟑
𝟑
)
• x = 2 + (
𝟔
𝟑
x 𝟑 )
• x = 2 + 2 𝟑
• x = 2 ( 1 + 𝟑 )
• The value of x, which satisfies the equation 2.8 x – 0.8 x = 9 is
a)
𝟓
𝟐
b)
𝟗
𝟐
c)
𝟐
𝟓
d)
𝟐
𝟗
Solution:
8 x – 0.8 x = 9
2 x = 9
a) 2 (
𝟓
𝟐
) = 𝟗
5  9
b) 2 (
𝟗
𝟐
) = 9
9 = 9
• One solution of the equation 2x + 3y = 10
a) x = 3 and y = 2
b) x = 2 and y = 3
c) x = 2 and y = 2
d) x = 10 and y = -10
Solution: a) x = 3 and y = 2
2 (3) + 3(2) = 10
6 + 6 = 10
12  10
b) x = 2 and y = 3
2 (2) + 3 (3) = 10
4 + 9 = 10
13 ≠ 𝟏𝟎
c) x = 2 and y = 2
2 (2) + 3 (2) = 10
4 + 6 = 10
10 = 10
• The solution of the equation x + 3y = 12 will be
a) (2,3)
b) (1,2)
c) (3,3)
d) (4,2)
Solution:
a) (x, y) = (2,3)
x + 3y = 12 → 2 + 3(3) = 12
→ 2 + 9 = 12
→ 𝟏𝟏 ≠ 𝟏𝟐
b) (x, y) = (1,2)
x + 3y = 12 → 𝟏 + 3(2) = 12
→ 1 + 6 = 12
→ 𝟕 ≠ 𝟏𝟐
c) (x, y) = (3,3)
x + 3y = 12 → 𝟑 + 3(3) = 12
→ 3 + 9 = 12
→ 𝟏𝟐 = 𝟏𝟐
Summary
• An equation of the form ax + by + c = 0, where a, b, c
are real numbers, such that a ≠ 0, b ≠ 0. Is called
linear equation in two variable.
• Substitution method - The substitution method is the
algebraic method to solve simultaneous linear
equations. As the word says, in this method, the
value of one variable from one equation is
substituted in the other equation.
Glossary
Equation
Equation is a mathematical statement which shows that the value of two expression
are equal.
Linear equation in one variable
An equation which has the variable with the highest power one is called a linear
equation in one variable
Linear equation in two variable
An equation which can be put in the form ax + by + c = 0. where a, b and c are real
numbers and a and b both are not equal to zero, is called a linear equation in two
variables.
Solution of a linear equation in one variable
The value of a variable for which the given equation becomes true is known as
“Solution” or “Root’ of the equation.
Solution of a linear equation in two variable
A solution of the linear equation in two variables is an ordered pair of numbers,
which satisfies the equations.
LETS PLAY
QUIZIZZ
Example
Find the four solutions of the equation 2x + 3y – 12 = 0
Solution –
The given equation can be written as : y =
𝟏𝟐 −𝟐𝒙
𝟑
y =
𝟏𝟐 −𝟐𝒙
𝟑
. . . . . . . . . . ( 1 )
On putting x = 0 in equation (1), we get
y =
𝟏𝟐 −𝟐 ( 𝟎 )
𝟑
y =
𝟏𝟐
𝟑
= 4
On putting x = 3 in equation (1), we get
y =
𝟏𝟐 −𝟐 (𝟑)
𝟑
y =
𝟔
𝟑
y = 2
On putting x = 6 in equation (1), we get
y =
𝟏𝟐 −𝟐 ( 𝟔 )
𝟑
y =
𝟏𝟐 −𝟏𝟐
𝟑
y = 0
On putting x = 9 in equation (1), we get
y =
𝟏𝟐 −𝟐 (𝟗)
𝟑
y =
𝟏𝟐 −𝟏𝟖
𝟑
y =
−𝟔
𝟑
y = -2
Hence, the four solutions of the given equation
are:
(i) x = 0, y = 4
(ii) x = 3, y = 2
(iii) x = 6, y = 0
(iv) x = 9, y = -3
A linear equation in two variables has infinitely
many solutions.
Test Your Knowledge
Equation p = 2q + 3 has _____________
a)only one solution.
b)only two solutions.
c)infinitely many solutions.
d)no solution.

Weitere ähnliche Inhalte

Was ist angesagt?

class 10 chapter 1- real numbers
class 10 chapter 1- real numbersclass 10 chapter 1- real numbers
class 10 chapter 1- real numberskaran saini
 
The remainder theorem powerpoint
The remainder theorem powerpointThe remainder theorem powerpoint
The remainder theorem powerpointJuwileene Soriano
 
Coordinate geometry
Coordinate geometry Coordinate geometry
Coordinate geometry Anju Soman
 
QUADRATIC EQUATIONS
QUADRATIC EQUATIONSQUADRATIC EQUATIONS
QUADRATIC EQUATIONShiratufail
 
2.6 Linear Inequalities in Two Variables
2.6 Linear Inequalities in Two Variables2.6 Linear Inequalities in Two Variables
2.6 Linear Inequalities in Two Variableshisema01
 
Rational expressions ppt
Rational expressions pptRational expressions ppt
Rational expressions pptDoreen Mhizha
 
quadratic equation
quadratic equationquadratic equation
quadratic equationRubal Oborai
 
CLASS X MATHS LINEAR EQUATIONS
CLASS X MATHS LINEAR EQUATIONSCLASS X MATHS LINEAR EQUATIONS
CLASS X MATHS LINEAR EQUATIONSRc Os
 
Rational Zeros and Decarte's Rule of Signs
Rational Zeros and Decarte's Rule of SignsRational Zeros and Decarte's Rule of Signs
Rational Zeros and Decarte's Rule of Signsswartzje
 
Exponents and power
Exponents and powerExponents and power
Exponents and powerNidhi Singh
 
Quadratic equations
Quadratic equationsQuadratic equations
Quadratic equationsMark Ryder
 
Completing the square
Completing the squareCompleting the square
Completing the squareRon Eick
 
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPTCLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT05092000
 
Inequalities ppt revised
Inequalities ppt revisedInequalities ppt revised
Inequalities ppt revisedtroxellm
 
Linear Equation In One Variable
Linear Equation In One VariableLinear Equation In One Variable
Linear Equation In One VariablePooja M
 

Was ist angesagt? (20)

class 10 chapter 1- real numbers
class 10 chapter 1- real numbersclass 10 chapter 1- real numbers
class 10 chapter 1- real numbers
 
The remainder theorem powerpoint
The remainder theorem powerpointThe remainder theorem powerpoint
The remainder theorem powerpoint
 
Rational numbers
Rational numbersRational numbers
Rational numbers
 
Coordinate geometry
Coordinate geometry Coordinate geometry
Coordinate geometry
 
QUADRATIC EQUATIONS
QUADRATIC EQUATIONSQUADRATIC EQUATIONS
QUADRATIC EQUATIONS
 
Polynomials
PolynomialsPolynomials
Polynomials
 
2.6 Linear Inequalities in Two Variables
2.6 Linear Inequalities in Two Variables2.6 Linear Inequalities in Two Variables
2.6 Linear Inequalities in Two Variables
 
COORDINATE GEOMETRY
COORDINATE GEOMETRYCOORDINATE GEOMETRY
COORDINATE GEOMETRY
 
Rational expressions ppt
Rational expressions pptRational expressions ppt
Rational expressions ppt
 
quadratic equation
quadratic equationquadratic equation
quadratic equation
 
CLASS X MATHS LINEAR EQUATIONS
CLASS X MATHS LINEAR EQUATIONSCLASS X MATHS LINEAR EQUATIONS
CLASS X MATHS LINEAR EQUATIONS
 
Rational Zeros and Decarte's Rule of Signs
Rational Zeros and Decarte's Rule of SignsRational Zeros and Decarte's Rule of Signs
Rational Zeros and Decarte's Rule of Signs
 
Exponents and power
Exponents and powerExponents and power
Exponents and power
 
Multiplying polynomials
Multiplying polynomialsMultiplying polynomials
Multiplying polynomials
 
Chapter 5 Point Slope Form
Chapter 5 Point Slope FormChapter 5 Point Slope Form
Chapter 5 Point Slope Form
 
Quadratic equations
Quadratic equationsQuadratic equations
Quadratic equations
 
Completing the square
Completing the squareCompleting the square
Completing the square
 
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPTCLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
CLASS 9 LINEAR EQUATIONS IN TWO VARIABLES PPT
 
Inequalities ppt revised
Inequalities ppt revisedInequalities ppt revised
Inequalities ppt revised
 
Linear Equation In One Variable
Linear Equation In One VariableLinear Equation In One Variable
Linear Equation In One Variable
 

Ähnlich wie MATHS - Linear equation in two variable (Class - X) Maharashtra Board

Business Math Chapter 3
Business Math Chapter 3Business Math Chapter 3
Business Math Chapter 3Nazrin Nazdri
 
Pair of linear equation in two variables
Pair of linear equation in two variables Pair of linear equation in two variables
Pair of linear equation in two variables shivangi gupta
 
Linear equations in two variables
Linear equations in two variablesLinear equations in two variables
Linear equations in two variablesVinisha Pathak
 
C2 st lecture 3 handout
C2 st lecture 3 handoutC2 st lecture 3 handout
C2 st lecture 3 handoutfatima d
 
Quarter 1 - Illustrating and solving quadratic equations
Quarter 1 - Illustrating and solving quadratic equationsQuarter 1 - Illustrating and solving quadratic equations
Quarter 1 - Illustrating and solving quadratic equationsReynz Anario
 
linearequns-classx-180912070018.pdf
linearequns-classx-180912070018.pdflinearequns-classx-180912070018.pdf
linearequns-classx-180912070018.pdfMayankYadav777500
 
Algebraic Simplification and evaluation
Algebraic Simplification and evaluationAlgebraic Simplification and evaluation
Algebraic Simplification and evaluationPuna Ripiye
 
Linear equation in 2 variable class 10
Linear equation in 2 variable class 10Linear equation in 2 variable class 10
Linear equation in 2 variable class 10AadhiSXA
 
Linear equation in one variable for class VIII by G R Ahmed
Linear equation in one variable for class VIII by G R Ahmed Linear equation in one variable for class VIII by G R Ahmed
Linear equation in one variable for class VIII by G R Ahmed MD. G R Ahmed
 
QUADRATIC EQUATIONS WITH MATHS PROPER VERIFY
QUADRATIC EQUATIONS WITH MATHS PROPER VERIFYQUADRATIC EQUATIONS WITH MATHS PROPER VERIFY
QUADRATIC EQUATIONS WITH MATHS PROPER VERIFYssuser2e348b
 
Linear equations Class 10 by aryan kathuria
Linear equations Class 10 by aryan kathuriaLinear equations Class 10 by aryan kathuria
Linear equations Class 10 by aryan kathuriaDhiraj Singh
 
Algebra Revision.ppt
Algebra Revision.pptAlgebra Revision.ppt
Algebra Revision.pptAaronChi5
 

Ähnlich wie MATHS - Linear equation in two variable (Class - X) Maharashtra Board (20)

Business Math Chapter 3
Business Math Chapter 3Business Math Chapter 3
Business Math Chapter 3
 
Chapter 2
Chapter  2Chapter  2
Chapter 2
 
Pair of linear equation in two variables
Pair of linear equation in two variables Pair of linear equation in two variables
Pair of linear equation in two variables
 
Linear equations in two variables
Linear equations in two variablesLinear equations in two variables
Linear equations in two variables
 
C2 st lecture 3 handout
C2 st lecture 3 handoutC2 st lecture 3 handout
C2 st lecture 3 handout
 
Quarter 1 - Illustrating and solving quadratic equations
Quarter 1 - Illustrating and solving quadratic equationsQuarter 1 - Illustrating and solving quadratic equations
Quarter 1 - Illustrating and solving quadratic equations
 
Algebra and functions review
Algebra and functions reviewAlgebra and functions review
Algebra and functions review
 
Algebra and functions review
Algebra and functions reviewAlgebra and functions review
Algebra and functions review
 
Algebra and functions review
Algebra and functions reviewAlgebra and functions review
Algebra and functions review
 
linear equations.pptx
linear equations.pptxlinear equations.pptx
linear equations.pptx
 
linearequns-classx-180912070018.pdf
linearequns-classx-180912070018.pdflinearequns-classx-180912070018.pdf
linearequns-classx-180912070018.pdf
 
Algebraic Simplification and evaluation
Algebraic Simplification and evaluationAlgebraic Simplification and evaluation
Algebraic Simplification and evaluation
 
Linear equation in 2 variable class 10
Linear equation in 2 variable class 10Linear equation in 2 variable class 10
Linear equation in 2 variable class 10
 
Mathematics ppt.pptx
Mathematics ppt.pptxMathematics ppt.pptx
Mathematics ppt.pptx
 
Linear equations in Two variables
Linear equations in Two variablesLinear equations in Two variables
Linear equations in Two variables
 
Linear equation in one variable for class VIII by G R Ahmed
Linear equation in one variable for class VIII by G R Ahmed Linear equation in one variable for class VIII by G R Ahmed
Linear equation in one variable for class VIII by G R Ahmed
 
QUADRATIC EQUATIONS WITH MATHS PROPER VERIFY
QUADRATIC EQUATIONS WITH MATHS PROPER VERIFYQUADRATIC EQUATIONS WITH MATHS PROPER VERIFY
QUADRATIC EQUATIONS WITH MATHS PROPER VERIFY
 
Maths
MathsMaths
Maths
 
Linear equations Class 10 by aryan kathuria
Linear equations Class 10 by aryan kathuriaLinear equations Class 10 by aryan kathuria
Linear equations Class 10 by aryan kathuria
 
Algebra Revision.ppt
Algebra Revision.pptAlgebra Revision.ppt
Algebra Revision.ppt
 

Mehr von Pooja M

Chapter 1 - Unit s and Measurement.pptx
Chapter 1 - Unit s and Measurement.pptxChapter 1 - Unit s and Measurement.pptx
Chapter 1 - Unit s and Measurement.pptxPooja M
 
Chapter 2 - Mechanical Properties of Fluids.pptx
Chapter 2 - Mechanical Properties of Fluids.pptxChapter 2 - Mechanical Properties of Fluids.pptx
Chapter 2 - Mechanical Properties of Fluids.pptxPooja M
 
Chapter 1 - Rotational Dynamics.pptx
Chapter 1 - Rotational Dynamics.pptxChapter 1 - Rotational Dynamics.pptx
Chapter 1 - Rotational Dynamics.pptxPooja M
 
Thermodynamics.ppt
Thermodynamics.pptThermodynamics.ppt
Thermodynamics.pptPooja M
 
Chapter 5 - Oscillation.pptx
Chapter 5 - Oscillation.pptxChapter 5 - Oscillation.pptx
Chapter 5 - Oscillation.pptxPooja M
 
Chapter 6 - Superposition of waves.pptx
Chapter 6 - Superposition of waves.pptxChapter 6 - Superposition of waves.pptx
Chapter 6 - Superposition of waves.pptxPooja M
 
Chapter 7 - Wave optics.pptx
Chapter 7 - Wave optics.pptxChapter 7 - Wave optics.pptx
Chapter 7 - Wave optics.pptxPooja M
 
Chapter 8 - Electrostatic.pptx
Chapter 8 - Electrostatic.pptxChapter 8 - Electrostatic.pptx
Chapter 8 - Electrostatic.pptxPooja M
 
Current Electricity.pptx
Current Electricity.pptxCurrent Electricity.pptx
Current Electricity.pptxPooja M
 
Chap 11 - Magnetic Materials.pptx
Chap 11 - Magnetic Materials.pptxChap 11 - Magnetic Materials.pptx
Chap 11 - Magnetic Materials.pptxPooja M
 
Chap 11 - ELECTRIC CURRENT THROUGH CONDUCTOR.pptx
Chap 11 - ELECTRIC CURRENT THROUGH CONDUCTOR.pptxChap 11 - ELECTRIC CURRENT THROUGH CONDUCTOR.pptx
Chap 11 - ELECTRIC CURRENT THROUGH CONDUCTOR.pptxPooja M
 
Chapter 16 - Semiconductor Devices.pptx
Chapter 16 - Semiconductor Devices.pptxChapter 16 - Semiconductor Devices.pptx
Chapter 16 - Semiconductor Devices.pptxPooja M
 
Chapter 9 - Prism, optical instruments (PHYSICS - CLASS XI)
Chapter 9 - Prism, optical instruments (PHYSICS - CLASS XI)Chapter 9 - Prism, optical instruments (PHYSICS - CLASS XI)
Chapter 9 - Prism, optical instruments (PHYSICS - CLASS XI)Pooja M
 
CLASS XI - Chapter 9 optics (MAHARASHRA STATE BOARD)
CLASS XI - Chapter 9   optics  (MAHARASHRA STATE BOARD)CLASS XI - Chapter 9   optics  (MAHARASHRA STATE BOARD)
CLASS XI - Chapter 9 optics (MAHARASHRA STATE BOARD)Pooja M
 
CLASSXII (PHYSICS) Chapter 10 electrostatics
CLASSXII (PHYSICS) Chapter 10   electrostaticsCLASSXII (PHYSICS) Chapter 10   electrostatics
CLASSXII (PHYSICS) Chapter 10 electrostaticsPooja M
 
PHYSICS CLASS XI Chapter 5 - gravitation
PHYSICS CLASS XI Chapter 5 - gravitationPHYSICS CLASS XI Chapter 5 - gravitation
PHYSICS CLASS XI Chapter 5 - gravitationPooja M
 
Chapter 4 laws of motion
Chapter 4   laws of motion Chapter 4   laws of motion
Chapter 4 laws of motion Pooja M
 
Chapter 2 mechanical properties of fluids
Chapter 2   mechanical properties of fluids Chapter 2   mechanical properties of fluids
Chapter 2 mechanical properties of fluids Pooja M
 
Chapter 16 semiconductor devices
Chapter 16   semiconductor devices Chapter 16   semiconductor devices
Chapter 16 semiconductor devices Pooja M
 
Chapter 3 motion in a plane
Chapter 3   motion in a plane Chapter 3   motion in a plane
Chapter 3 motion in a plane Pooja M
 

Mehr von Pooja M (20)

Chapter 1 - Unit s and Measurement.pptx
Chapter 1 - Unit s and Measurement.pptxChapter 1 - Unit s and Measurement.pptx
Chapter 1 - Unit s and Measurement.pptx
 
Chapter 2 - Mechanical Properties of Fluids.pptx
Chapter 2 - Mechanical Properties of Fluids.pptxChapter 2 - Mechanical Properties of Fluids.pptx
Chapter 2 - Mechanical Properties of Fluids.pptx
 
Chapter 1 - Rotational Dynamics.pptx
Chapter 1 - Rotational Dynamics.pptxChapter 1 - Rotational Dynamics.pptx
Chapter 1 - Rotational Dynamics.pptx
 
Thermodynamics.ppt
Thermodynamics.pptThermodynamics.ppt
Thermodynamics.ppt
 
Chapter 5 - Oscillation.pptx
Chapter 5 - Oscillation.pptxChapter 5 - Oscillation.pptx
Chapter 5 - Oscillation.pptx
 
Chapter 6 - Superposition of waves.pptx
Chapter 6 - Superposition of waves.pptxChapter 6 - Superposition of waves.pptx
Chapter 6 - Superposition of waves.pptx
 
Chapter 7 - Wave optics.pptx
Chapter 7 - Wave optics.pptxChapter 7 - Wave optics.pptx
Chapter 7 - Wave optics.pptx
 
Chapter 8 - Electrostatic.pptx
Chapter 8 - Electrostatic.pptxChapter 8 - Electrostatic.pptx
Chapter 8 - Electrostatic.pptx
 
Current Electricity.pptx
Current Electricity.pptxCurrent Electricity.pptx
Current Electricity.pptx
 
Chap 11 - Magnetic Materials.pptx
Chap 11 - Magnetic Materials.pptxChap 11 - Magnetic Materials.pptx
Chap 11 - Magnetic Materials.pptx
 
Chap 11 - ELECTRIC CURRENT THROUGH CONDUCTOR.pptx
Chap 11 - ELECTRIC CURRENT THROUGH CONDUCTOR.pptxChap 11 - ELECTRIC CURRENT THROUGH CONDUCTOR.pptx
Chap 11 - ELECTRIC CURRENT THROUGH CONDUCTOR.pptx
 
Chapter 16 - Semiconductor Devices.pptx
Chapter 16 - Semiconductor Devices.pptxChapter 16 - Semiconductor Devices.pptx
Chapter 16 - Semiconductor Devices.pptx
 
Chapter 9 - Prism, optical instruments (PHYSICS - CLASS XI)
Chapter 9 - Prism, optical instruments (PHYSICS - CLASS XI)Chapter 9 - Prism, optical instruments (PHYSICS - CLASS XI)
Chapter 9 - Prism, optical instruments (PHYSICS - CLASS XI)
 
CLASS XI - Chapter 9 optics (MAHARASHRA STATE BOARD)
CLASS XI - Chapter 9   optics  (MAHARASHRA STATE BOARD)CLASS XI - Chapter 9   optics  (MAHARASHRA STATE BOARD)
CLASS XI - Chapter 9 optics (MAHARASHRA STATE BOARD)
 
CLASSXII (PHYSICS) Chapter 10 electrostatics
CLASSXII (PHYSICS) Chapter 10   electrostaticsCLASSXII (PHYSICS) Chapter 10   electrostatics
CLASSXII (PHYSICS) Chapter 10 electrostatics
 
PHYSICS CLASS XI Chapter 5 - gravitation
PHYSICS CLASS XI Chapter 5 - gravitationPHYSICS CLASS XI Chapter 5 - gravitation
PHYSICS CLASS XI Chapter 5 - gravitation
 
Chapter 4 laws of motion
Chapter 4   laws of motion Chapter 4   laws of motion
Chapter 4 laws of motion
 
Chapter 2 mechanical properties of fluids
Chapter 2   mechanical properties of fluids Chapter 2   mechanical properties of fluids
Chapter 2 mechanical properties of fluids
 
Chapter 16 semiconductor devices
Chapter 16   semiconductor devices Chapter 16   semiconductor devices
Chapter 16 semiconductor devices
 
Chapter 3 motion in a plane
Chapter 3   motion in a plane Chapter 3   motion in a plane
Chapter 3 motion in a plane
 

Kürzlich hochgeladen

How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17Celine George
 
Textual Evidence in Reading and Writing of SHS
Textual Evidence in Reading and Writing of SHSTextual Evidence in Reading and Writing of SHS
Textual Evidence in Reading and Writing of SHSMae Pangan
 
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...Nguyen Thanh Tu Collection
 
Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4JOYLYNSAMANIEGO
 
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)lakshayb543
 
Concurrency Control in Database Management system
Concurrency Control in Database Management systemConcurrency Control in Database Management system
Concurrency Control in Database Management systemChristalin Nelson
 
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATIONTHEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATIONHumphrey A Beña
 
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptxQ4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptxlancelewisportillo
 
Narcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdfNarcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdfPrerana Jadhav
 
Grade 9 Quarter 4 Dll Grade 9 Quarter 4 DLL.pdf
Grade 9 Quarter 4 Dll Grade 9 Quarter 4 DLL.pdfGrade 9 Quarter 4 Dll Grade 9 Quarter 4 DLL.pdf
Grade 9 Quarter 4 Dll Grade 9 Quarter 4 DLL.pdfJemuel Francisco
 
ROLES IN A STAGE PRODUCTION in arts.pptx
ROLES IN A STAGE PRODUCTION in arts.pptxROLES IN A STAGE PRODUCTION in arts.pptx
ROLES IN A STAGE PRODUCTION in arts.pptxVanesaIglesias10
 
Multi Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP ModuleMulti Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP ModuleCeline George
 
Measures of Position DECILES for ungrouped data
Measures of Position DECILES for ungrouped dataMeasures of Position DECILES for ungrouped data
Measures of Position DECILES for ungrouped dataBabyAnnMotar
 
Mental Health Awareness - a toolkit for supporting young minds
Mental Health Awareness - a toolkit for supporting young mindsMental Health Awareness - a toolkit for supporting young minds
Mental Health Awareness - a toolkit for supporting young mindsPooky Knightsmith
 
How to Make a Duplicate of Your Odoo 17 Database
How to Make a Duplicate of Your Odoo 17 DatabaseHow to Make a Duplicate of Your Odoo 17 Database
How to Make a Duplicate of Your Odoo 17 DatabaseCeline George
 
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptxMULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptxAnupkumar Sharma
 
4.11.24 Mass Incarceration and the New Jim Crow.pptx
4.11.24 Mass Incarceration and the New Jim Crow.pptx4.11.24 Mass Incarceration and the New Jim Crow.pptx
4.11.24 Mass Incarceration and the New Jim Crow.pptxmary850239
 

Kürzlich hochgeladen (20)

How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17
 
Textual Evidence in Reading and Writing of SHS
Textual Evidence in Reading and Writing of SHSTextual Evidence in Reading and Writing of SHS
Textual Evidence in Reading and Writing of SHS
 
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...
31 ĐỀ THI THỬ VÀO LỚP 10 - TIẾNG ANH - FORM MỚI 2025 - 40 CÂU HỎI - BÙI VĂN V...
 
Mattingly "AI & Prompt Design: Large Language Models"
Mattingly "AI & Prompt Design: Large Language Models"Mattingly "AI & Prompt Design: Large Language Models"
Mattingly "AI & Prompt Design: Large Language Models"
 
Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4
 
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
 
Faculty Profile prashantha K EEE dept Sri Sairam college of Engineering
Faculty Profile prashantha K EEE dept Sri Sairam college of EngineeringFaculty Profile prashantha K EEE dept Sri Sairam college of Engineering
Faculty Profile prashantha K EEE dept Sri Sairam college of Engineering
 
Concurrency Control in Database Management system
Concurrency Control in Database Management systemConcurrency Control in Database Management system
Concurrency Control in Database Management system
 
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATIONTHEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
 
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptxQ4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
 
Narcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdfNarcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdf
 
Grade 9 Quarter 4 Dll Grade 9 Quarter 4 DLL.pdf
Grade 9 Quarter 4 Dll Grade 9 Quarter 4 DLL.pdfGrade 9 Quarter 4 Dll Grade 9 Quarter 4 DLL.pdf
Grade 9 Quarter 4 Dll Grade 9 Quarter 4 DLL.pdf
 
ROLES IN A STAGE PRODUCTION in arts.pptx
ROLES IN A STAGE PRODUCTION in arts.pptxROLES IN A STAGE PRODUCTION in arts.pptx
ROLES IN A STAGE PRODUCTION in arts.pptx
 
Multi Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP ModuleMulti Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP Module
 
Measures of Position DECILES for ungrouped data
Measures of Position DECILES for ungrouped dataMeasures of Position DECILES for ungrouped data
Measures of Position DECILES for ungrouped data
 
Mental Health Awareness - a toolkit for supporting young minds
Mental Health Awareness - a toolkit for supporting young mindsMental Health Awareness - a toolkit for supporting young minds
Mental Health Awareness - a toolkit for supporting young minds
 
INCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptx
INCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptxINCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptx
INCLUSIVE EDUCATION PRACTICES FOR TEACHERS AND TRAINERS.pptx
 
How to Make a Duplicate of Your Odoo 17 Database
How to Make a Duplicate of Your Odoo 17 DatabaseHow to Make a Duplicate of Your Odoo 17 Database
How to Make a Duplicate of Your Odoo 17 Database
 
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptxMULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
 
4.11.24 Mass Incarceration and the New Jim Crow.pptx
4.11.24 Mass Incarceration and the New Jim Crow.pptx4.11.24 Mass Incarceration and the New Jim Crow.pptx
4.11.24 Mass Incarceration and the New Jim Crow.pptx
 

MATHS - Linear equation in two variable (Class - X) Maharashtra Board

  • 1.
  • 2. • 5x • 2x – 3 • 3x + y • 2xy + 5 • xyz + x + y + z • x2 + 1 • y + y2 Some examples of expressions
  • 4. • 5x = 25 • 2x – 3 = 9 • 2y + 𝟓 𝟐 = 8 • 6z + 10 = -7 • 9x – 11 = 8 Some examples of equations
  • 5. Equations use the equality (=) sign If yes = equation  If no = equation 
  • 6. These are linear expressions: • 2x • 2x + 1 • 3y – 7 • 12 – 5z These are not linear expressions • 𝑥2 + 1 • y+𝑦2 • 1+z+𝑧2 +𝑧3 (since highest power of variable > 1) A linear expression is an expression whose highest power of the variable is one only.
  • 7. Linear Equations The equation of a straight line is the linear equation. It could be in one variable or two variables. Linear Equation in One Variable If there is only one variable in the equation then it is called a linear equation in one variable. The general form is ax + b = c, where a, b and c are real numbers and a ≠ 0.
  • 8. Example x + 5 = 10 y – 3 = 19 These are called linear equations in one variable because the highest degree of the variable is one and there is only one variable.
  • 9. • We assume that the two sides of the equation are balanced. • We perform the same mathematical operations on both sides of the equation, so that the balance is not disturbed. How to find the solution of an equation?
  • 10. X + 3 = 7 X = 7 The value which when substituted for the variable in the equation, makes its two sides equal, is called a solution ( or root ) of the equation.
  • 11. REMEMBER • The same number can be added to both the sides of the equation. • The same number can be subtracted from both the sides of the equation. • We can multiply or divide both the sides of the equation by the same non-zero number.
  • 13. • Solve the linear equation: 4x + 3 = 15 – 2x Solution: 4x + 3 = 15 – 2x On subtracting 3 from both the sides, we get 4x + 3 – 3 = 15 – 2x – 3 Or, 4x = 12 – 2x 4x + 2x = 12 – 2x + 2x 6x = 12 𝟔𝒙 𝟔 = 𝟏𝟐 𝟔 X = 2 Hence, x = 2 is the solution of the given solution.
  • 14. MATHEMATICS – I CHAPTER – 1 LINEAR EUATIONS IN TWO VARIABLES CLASS X
  • 15. • ax + b = c, where a, b and c are real numbers and a ≠ 0. Example , 2x + 3 = 6 • ax + by + c = 0, where a, b and are real numbers, such that a ≠ 0, b ≠ 0. Example, 2x + 5y + 8 = 0 Linear equation in one variable Linear equation in two variable
  • 16. ax + by + c = 0, where a, b and c are real numbers, such that a ≠ 0, b ≠ 0. Example: a) 4x + 3y = 4 b) -3x + 7 = 5y c) X = 4y d) Y = 2 – 3x
  • 17. • Compare the equation ax + by + c = 0 with equation 2x + 3y = 4.37 and find the values of a, b and c? a)a = 2, b = 3 and c = 4.37 b)a = 2, b = 3 and c = - 4.37 c)a = 2, b = -3 and c = - 4.37 d)a = -2, b = 3 and c = 4.37 Solution: b) a = 2, b = 3 and c = - 4.37 ax + by + c = 0 2x + 3y + (-4.37) = 0
  • 18. Solution of a linear equations in two variable The solution of a linear equation in two variables is an ordered pair of numbers, which satisfies the equation. The values x = m and y = n are said to be the solution of the linear equation. ‘ax + by + c = 0’ if am + bn + c = 0
  • 19. • Show that x = 4 and y = -1 satisfy the equation x + 3y – 1 = 0 Solution: On substituting x = 4 and y = -1 in equation x + 3y – 1 = 0, we get L. H. S = 4 + 3 X (-1) – 1 = 4 – 3 – 1 = 0 = R. H. S Hence, x = 4 and y = -1 satisfy the equation x + 3y – 1 = 0.
  • 21. Oranges Apples Fruits 1 9 10 2 8 10 3 7 10 4 6 10 5 5 10 6 4 10 7 3 10 8 2 10 9 1 10 Hit and Trial Method
  • 22. Hint – Apples are 2 more than oranges 6 Apples + 4 Oranges = 10 6 Apples – 4 Oranges = 2 x + y = 10 x – y = 2 (2 – Equations, 2 – Variables or 2 – Unknowns) This pair of equation is called linear of equation in two variables or System of equation or simultaneous equations. Algebraic or Graphical Method.
  • 23.
  • 24. • If x = 1, y = 2 is a solution of the equation 3x + 2y = k, then the value of k is a) 7 b) 6 c) 5 d) 4 Solution: 3x + 2y = k 3 (1) + 2 (2) = k 3 + 4 = k K = 7
  • 25. • 𝑻𝒉𝒆 𝒄𝒐𝒎𝒎𝒐𝒏 𝒔𝒐𝒍𝒖𝒕𝒊𝒐𝒏 𝒐𝒇 𝟑𝒙 + 𝟐𝒚 = 𝟔 𝒂𝒏𝒅 𝟓𝒙 − 𝟐𝒚 = 𝟏𝟎 𝒊𝒔 a)(0,3) b)(0,-5) c)(2,0) d)(1,0) Solution: 3x + 2y = 6 5x – 2y = 10 + ------------------------------- 8 x + 0 = 16 x = 𝟏𝟔 𝟖 = 2 3x + 2y = 6 3 (2) + 2y = 6 6 + 2y = 6 2y = 6 – 6 2y = 0 Y = 0 (x, y) = (2,0)
  • 26. • Solution of the linear equation (x-1) = ( 𝟑 𝟒 )(x+1) – ( 𝟏 𝟐 ) will be a) x = 5 b)x = 4 c) x = 3 d)x = 1 Solution: (x-1) = ( 𝟑 𝟒 )(x+1) – ( 𝟏 𝟐 ) x – 1 = 𝟑 𝟒 x + 𝟑 𝟒 - 𝟏 𝟐 x - 𝟑 𝟒 x = 𝟑 𝟒 - 𝟏 𝟐 + 1 𝒙(𝟒−𝟑) 𝟒 = (𝟔−𝟒) 𝟖 + 1 𝒙 𝟒 = 𝟐 𝟖 + 1 2x = 2 + 8 2x = 10 X = 5
  • 27. • What is the value of x in the equation 𝟑 x – 2 = 2 𝟑 + 4 a) 2 ( 1 - 𝟑 ) b) 2 ( 1 + 𝟑 ) c) 1 + 𝟑 d) 1 - 𝟑 Solution – 𝟑 x – 2 = 2 𝟑 + 4 • 𝟑 x = 2 𝟑 + 4 + 2 • 𝟑 x = 2 𝟑 + 6 • 𝟑 𝟑 x = 𝟐 𝟑+ 𝟔 𝟑 • x = 2 + 𝟔 𝟑 • x = 2 + ( 𝟔 𝟑 x 𝟑 𝟑 ) • x = 2 + ( 𝟔 𝟑 x 𝟑 ) • x = 2 + 2 𝟑 • x = 2 ( 1 + 𝟑 )
  • 28. • The value of x, which satisfies the equation 2.8 x – 0.8 x = 9 is a) 𝟓 𝟐 b) 𝟗 𝟐 c) 𝟐 𝟓 d) 𝟐 𝟗 Solution: 8 x – 0.8 x = 9 2 x = 9 a) 2 ( 𝟓 𝟐 ) = 𝟗 5  9 b) 2 ( 𝟗 𝟐 ) = 9 9 = 9
  • 29. • One solution of the equation 2x + 3y = 10 a) x = 3 and y = 2 b) x = 2 and y = 3 c) x = 2 and y = 2 d) x = 10 and y = -10 Solution: a) x = 3 and y = 2 2 (3) + 3(2) = 10 6 + 6 = 10 12  10 b) x = 2 and y = 3 2 (2) + 3 (3) = 10 4 + 9 = 10 13 ≠ 𝟏𝟎 c) x = 2 and y = 2 2 (2) + 3 (2) = 10 4 + 6 = 10 10 = 10
  • 30. • The solution of the equation x + 3y = 12 will be a) (2,3) b) (1,2) c) (3,3) d) (4,2) Solution: a) (x, y) = (2,3) x + 3y = 12 → 2 + 3(3) = 12 → 2 + 9 = 12 → 𝟏𝟏 ≠ 𝟏𝟐 b) (x, y) = (1,2) x + 3y = 12 → 𝟏 + 3(2) = 12 → 1 + 6 = 12 → 𝟕 ≠ 𝟏𝟐 c) (x, y) = (3,3) x + 3y = 12 → 𝟑 + 3(3) = 12 → 3 + 9 = 12 → 𝟏𝟐 = 𝟏𝟐
  • 31. Summary • An equation of the form ax + by + c = 0, where a, b, c are real numbers, such that a ≠ 0, b ≠ 0. Is called linear equation in two variable. • Substitution method - The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
  • 32. Glossary Equation Equation is a mathematical statement which shows that the value of two expression are equal. Linear equation in one variable An equation which has the variable with the highest power one is called a linear equation in one variable Linear equation in two variable An equation which can be put in the form ax + by + c = 0. where a, b and c are real numbers and a and b both are not equal to zero, is called a linear equation in two variables. Solution of a linear equation in one variable The value of a variable for which the given equation becomes true is known as “Solution” or “Root’ of the equation. Solution of a linear equation in two variable A solution of the linear equation in two variables is an ordered pair of numbers, which satisfies the equations.
  • 34.
  • 35. Example Find the four solutions of the equation 2x + 3y – 12 = 0 Solution – The given equation can be written as : y = 𝟏𝟐 −𝟐𝒙 𝟑 y = 𝟏𝟐 −𝟐𝒙 𝟑 . . . . . . . . . . ( 1 ) On putting x = 0 in equation (1), we get y = 𝟏𝟐 −𝟐 ( 𝟎 ) 𝟑 y = 𝟏𝟐 𝟑 = 4 On putting x = 3 in equation (1), we get y = 𝟏𝟐 −𝟐 (𝟑) 𝟑 y = 𝟔 𝟑 y = 2
  • 36. On putting x = 6 in equation (1), we get y = 𝟏𝟐 −𝟐 ( 𝟔 ) 𝟑 y = 𝟏𝟐 −𝟏𝟐 𝟑 y = 0 On putting x = 9 in equation (1), we get y = 𝟏𝟐 −𝟐 (𝟗) 𝟑 y = 𝟏𝟐 −𝟏𝟖 𝟑 y = −𝟔 𝟑 y = -2
  • 37. Hence, the four solutions of the given equation are: (i) x = 0, y = 4 (ii) x = 3, y = 2 (iii) x = 6, y = 0 (iv) x = 9, y = -3 A linear equation in two variables has infinitely many solutions.
  • 38. Test Your Knowledge Equation p = 2q + 3 has _____________ a)only one solution. b)only two solutions. c)infinitely many solutions. d)no solution.