Diese Präsentation wurde erfolgreich gemeldet.
Die SlideShare-Präsentation wird heruntergeladen. ×

Linear equations in Two Variable

Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Wird geladen in …3
×

Hier ansehen

1 von 14 Anzeige
Anzeige

Weitere Verwandte Inhalte

Diashows für Sie (20)

Ähnlich wie Linear equations in Two Variable (20)

Anzeige

Aktuellste (20)

Anzeige

Linear equations in Two Variable

  1. 1. Presented By:- Abhinav Somani
  2. 2. System Of Equations • A pair of Linear equation in two variables is said to form a system of linear equation. • For Example:-  2x-3y+9=0  x+4y+2=0 • These Equations form a system of Two Linear Equations in variables x and y.
  3. 3. General form of linear equations in two variables • The general form of a linear equation in two variables x and y is ax + by + c = 0, a and b is not equal to zero, where a, b and c being real numbers. • A solution of such an equation is a pair of values, One for x and the other for y, Which makes two sides of the equation equal. Every linear equation in two variables has infinitely many solutions which can be represented on a certain line.
  4. 4. Graphical Solutions of a Linear Equations • Let us consider the following system of two simultaneous linear equations in two variable.  2x+y-8=0  2x-5y+4=0 • Here we assign any value to one of the two variables and then determine the value of the other variable from the given equation
  5. 5. Solving Equations 1. 2x+y-8=0 X 4 0 Y 0 8 2. 2x-5y+4=0 X -2 0 Y 0 4/5 • 2x+y=8 2x+0=8 x=8/4 x=2 • 2x+y=8 2x0+y=8 0+y=8 y=8 • 2x-5y= -4 2x-5x0= -4 2x-0= -4 x= -2 • 2x-5y= -4 2x0-5y= -4 0-5y= -4 y=4/5
  6. 6. Algebraic Methods of Solving Simultaneous Linear Equations • The most commonly used algebraic methods of solving simultaneous linear equations in two variables are:-  Method of Elimination by substitution  Method of Elimination by equating the coefficient. Method of Cross Multiplication.
  7. 7. Elimination by substitution • Obtain the two equations. Let the equations be a1x+b1y+c1=0 (i) a2x+b2y+c2=0 (ii) • Choose either of the two equations say (i) and find the value of one variable say ‘y’ in terms of x. • Substitute the value of y, obtained in the previous step in equation (ii) to get an equation in x.
  8. 8. • Solve the equation obtained in the previous step to get the value of x. • Substitute the value of x and get the value of y. Let us take an example x+2y=-1 (i) 2x-3y=12 (ii)  For (i) equation 1. x+2y=-1 x=-2y-1 (iii)
  9. 9. • Substituting the value of x in equation (ii), we get 2x-3y=12 2(-2y-1) -3y=12 -4y-2-3y=12 -4y-3y=12+2 -7y=14 y=-2
  10. 10. • Putting the value of y in equation (iii) we get x=-2(-2)-1 x= 4-1 x=3
  11. 11. Elimination Method • In this method we eliminate one of the two variables to obtain an equation in one variable which can easily be solved. • Putting the value of the variable in any of the given equations. The value of the other variable can be obtained. • For example:- 3x+2y=11 2x+3y=4
  12. 12. • Let 3x+2y=11 (i) 2x+3y=4 (ii) • Multiply 3 in equation (i) and 2 in equation (ii) and subtracting equation (iv) from (iii), we get 9x+6y=33 (iii) 4x+6y=8 (iv) 5x =25 x=5
  13. 13. • Putting the value of x in equation (ii) we get, 2x+3y=4 2x5+3y=4 10+3y=4 3y=4-10 3y=-6 y=-2

×