1 von 30

## Was ist angesagt?

5.6 Parallel & Perpendicular Lines
5.6 Parallel & Perpendicular Linesvmonacelli

1.4.4 Parallel and Perpendicular Line Equations
1.4.4 Parallel and Perpendicular Line Equationssmiller5

Linear functions
Linear functionshalcr1ja

Systems of linear equations
Systems of linear equationsgandhinagar

Identifying slope and y intercept
Identifying slope and y interceptrobertleichner

Rational Zeros and Decarte's Rule of Signs
Rational Zeros and Decarte's Rule of Signsswartzje

Writing Equations of a Line
Writing Equations of a Lineswartzje

Parallel and Perpendicular Slopes lines
Parallel and Perpendicular Slopes linesswartzje

Polynomial functionsandgraphs
Polynomial functionsandgraphsJerlyn Fernandez

16.4 solving quadratics by completing the square
16.4 solving quadratics by completing the squareswartzje

Finding Slope Given A Graph And Two Points
Finding Slope Given A Graph And Two PointsGillian Guiang

Completing the Square
Completing the Squaretoni dimella

8.1 intro to functions
8.1 intro to functionsBarbara Knab

Radian and degree measure.Kiran S B

### Was ist angesagt?(20)

5.6 Parallel & Perpendicular Lines
5.6 Parallel & Perpendicular Lines

1.4.4 Parallel and Perpendicular Line Equations
1.4.4 Parallel and Perpendicular Line Equations

Linear functions
Linear functions

Systems of linear equations
Systems of linear equations

Identifying slope and y intercept
Identifying slope and y intercept

Rational Zeros and Decarte's Rule of Signs
Rational Zeros and Decarte's Rule of Signs

Writing Equations of a Line
Writing Equations of a Line

Parallel and Perpendicular Slopes lines
Parallel and Perpendicular Slopes lines

Polynomial functionsandgraphs
Polynomial functionsandgraphs

16.4 solving quadratics by completing the square
16.4 solving quadratics by completing the square

Binomial expansion
Binomial expansion

Polynomials
Polynomials

Chapter 5 Slope-Intercept Form
Chapter 5 Slope-Intercept Form

Finding Slope Given A Graph And Two Points
Finding Slope Given A Graph And Two Points

Completing the Square
Completing the Square

8.1 intro to functions
8.1 intro to functions

Operations on Real Numbers
Operations on Real Numbers

## Andere mochten auch

Pythagorean Theorem
Pythagorean Theoremalikaakean

13.cartesian coordinates

Rectangular coordinate system
Rectangular coordinate systemCathy Francisco

Higher Maths 1.1 - Straight Line
Higher Maths 1.1 - Straight Linetimschmitz

Straight Lines ( Especially For XI )
Straight Lines ( Especially For XI ) Atit Gaonkar

cartesian plane by : joe olivare
cartesian plane by : joe olivareJoe Olivare

Math unit28 straight lines
Math unit28 straight lineseLearningJa

F4 05 The Straight Line
F4 05 The Straight Lineguestcc333c

Hoag Ordered Pairs Lesson

Sequence and series
Sequence and seriesviannafaye

Arithmetic sequence
Arithmetic sequenceLeah Mel

Sequence powerpoint
Sequence powerpointcomlabfolder

Equations of Straight Lines
Equations of Straight Linesitutor

Equations of a line ppt
Equations of a line pptchriscline1979

Coordinates powerpoint
Coordinates powerpointkatielianne

Equation of the line
Equation of the lineEdgardo Mata

### Andere mochten auch(20)

Pythagorean Theorem
Pythagorean Theorem

13.cartesian coordinates
13.cartesian coordinates

Rectangular coordinate system
Rectangular coordinate system

Higher Maths 1.1 - Straight Line
Higher Maths 1.1 - Straight Line

Straight Lines ( Especially For XI )
Straight Lines ( Especially For XI )

cartesian plane by : joe olivare
cartesian plane by : joe olivare

Math unit28 straight lines
Math unit28 straight lines

F4 05 The Straight Line
F4 05 The Straight Line

Hoag Ordered Pairs Lesson
Hoag Ordered Pairs Lesson

Coordinate plane ppt
Coordinate plane ppt

Sequence and series
Sequence and series

Rectangular coordinate system
Rectangular coordinate system

Arithmetic sequence
Arithmetic sequence

Sequence powerpoint
Sequence powerpoint

Cartesian plane
Cartesian plane

Equations of Straight Lines
Equations of Straight Lines

Equations of a line ppt
Equations of a line ppt

Coordinates powerpoint
Coordinates powerpoint

Arithmetic Sequences
Arithmetic Sequences

Equation of the line
Equation of the line

## Ähnlich wie Solving Systems of Linear Equations Graphically

chapter1_part2.pdf
chapter1_part2.pdfAliEb2

Module 1 plane coordinate geometry
Module 1 plane coordinate geometrydionesioable

Solving Linear Equations
Solving Linear Equationstaco40

Algebra i ccp quarter 3 benchmark review 2013 (2)
Algebra i ccp quarter 3 benchmark review 2013 (2)MsKendall

7 1solve By Graphing
7 1solve By Graphingtaco40

Linear equations

January18
January18khyps13

Linear equations Class 10 by aryan kathuria
Linear equations Class 10 by aryan kathuriaDhiraj Singh

Linear equation in two variable
Linear equation in two variableRamjas College

Lecture 11 systems of nonlinear equations
Lecture 11 systems of nonlinear equationsHazel Joy Chong

Final presentation
Final presentationpaezp

Mathematics 8 Systems of Linear Inequalities
Mathematics 8 Systems of Linear InequalitiesJuan Miguel Palero

Maths coordinate geometry formulas.
Maths coordinate geometry formulas.tahmiinaaoxo

Standard form solve equations
Standard form solve equationspfefferteacher

WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptxKristenHathcock

### Ähnlich wie Solving Systems of Linear Equations Graphically(20)

chapter1_part2.pdf
chapter1_part2.pdf

Module 1 plane coordinate geometry
Module 1 plane coordinate geometry

Solving Linear Equations
Solving Linear Equations

Algebra i ccp quarter 3 benchmark review 2013 (2)
Algebra i ccp quarter 3 benchmark review 2013 (2)

7 1solve By Graphing
7 1solve By Graphing

Dec 14
Dec 14

Linear equations
Linear equations

January18
January18

Linear equations Class 10 by aryan kathuria
Linear equations Class 10 by aryan kathuria

Linear equation in two variable
Linear equation in two variable

Lecture 11 systems of nonlinear equations
Lecture 11 systems of nonlinear equations

7.4
7.4

Final presentation
Final presentation

Mathematics 8 Systems of Linear Inequalities
Mathematics 8 Systems of Linear Inequalities

Maths
Maths

Maths coordinate geometry formulas.
Maths coordinate geometry formulas.

Linear equations
Linear equations

Persamaan fungsi linier
Persamaan fungsi linier

Standard form solve equations
Standard form solve equations

WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx

## Mehr von florian Manzanilla

### Mehr von florian Manzanilla(7)

Hypothesis Testing
Hypothesis Testing

Math puzzles
Math puzzles

Social arithmetic
Social arithmetic

Ratio
Ratio

Proportion
Proportion

Proportion
Proportion

Solution of linear equation & inequality
Solution of linear equation & inequality

4.9.24 School Desegregation in Boston.pptx
4.9.24 School Desegregation in Boston.pptxmary850239

4.4.24 Economic Precarity and Global Economic Forces.pptx
4.4.24 Economic Precarity and Global Economic Forces.pptxmary850239

CLASSIFICATION OF ANTI - CANCER DRUGS.pptx
CLASSIFICATION OF ANTI - CANCER DRUGS.pptxAnupam32727

18. Training and prunning of horicultural crops.pptx
18. Training and prunning of horicultural crops.pptxUmeshTimilsina1

BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...Nguyen Thanh Tu Collection

ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6Vanessa Camilleri

Sarah Lahm In Media Res Media Component
Sarah Lahm In Media Res Media ComponentInMediaRes1

Employablity presentation and Future Career Plan.pptx
Employablity presentation and Future Career Plan.pptxryandux83rd

Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...Osopher

CHUYÊN ĐỀ ÔN THEO CÂU CHO HỌC SINH LỚP 12 ĐỂ ĐẠT ĐIỂM 5+ THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN THEO CÂU CHO HỌC SINH LỚP 12 ĐỂ ĐẠT ĐIỂM 5+ THI TỐT NGHIỆP THPT ...Nguyen Thanh Tu Collection

Jordan Chrietzberg In Media Res Media Component
Jordan Chrietzberg In Media Res Media ComponentInMediaRes1

LEVERAGING SYNERGISM INDUSTRY-ACADEMIA PARTNERSHIP FOR IMPLEMENTATION OF NAT...
LEVERAGING SYNERGISM INDUSTRY-ACADEMIA PARTNERSHIP FOR IMPLEMENTATION OF NAT...pragatimahajan3

The role of Geography in climate education: science and active citizenship
The role of Geography in climate education: science and active citizenshipKarl Donert

DBMSArchitecture_QueryProcessingandOptimization.pdf
DBMSArchitecture_QueryProcessingandOptimization.pdfChristalin Nelson

The Shop Floor Overview in the Odoo 17 ERP
The Shop Floor Overview in the Odoo 17 ERPCeline George

Scientific Writing :Research Discourse
Scientific Writing :Research DiscourseAnita GoswamiGiri

4.9.24 School Desegregation in Boston.pptx
4.9.24 School Desegregation in Boston.pptx

4.4.24 Economic Precarity and Global Economic Forces.pptx
4.4.24 Economic Precarity and Global Economic Forces.pptx

Chi-Square Test Non Parametric Test Categorical Variable
Chi-Square Test Non Parametric Test Categorical Variable

CLASSIFICATION OF ANTI - CANCER DRUGS.pptx
CLASSIFICATION OF ANTI - CANCER DRUGS.pptx

18. Training and prunning of horicultural crops.pptx
18. Training and prunning of horicultural crops.pptx

BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...

ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6

Sarah Lahm In Media Res Media Component
Sarah Lahm In Media Res Media Component

Employablity presentation and Future Career Plan.pptx
Employablity presentation and Future Career Plan.pptx

Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...

CHUYÊN ĐỀ ÔN THEO CÂU CHO HỌC SINH LỚP 12 ĐỂ ĐẠT ĐIỂM 5+ THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN THEO CÂU CHO HỌC SINH LỚP 12 ĐỂ ĐẠT ĐIỂM 5+ THI TỐT NGHIỆP THPT ...

Jordan Chrietzberg In Media Res Media Component
Jordan Chrietzberg In Media Res Media Component

LEVERAGING SYNERGISM INDUSTRY-ACADEMIA PARTNERSHIP FOR IMPLEMENTATION OF NAT...
LEVERAGING SYNERGISM INDUSTRY-ACADEMIA PARTNERSHIP FOR IMPLEMENTATION OF NAT...

The role of Geography in climate education: science and active citizenship
The role of Geography in climate education: science and active citizenship

DBMSArchitecture_QueryProcessingandOptimization.pdf
DBMSArchitecture_QueryProcessingandOptimization.pdf

The Shop Floor Overview in the Odoo 17 ERP
The Shop Floor Overview in the Odoo 17 ERP

Scientific Writing :Research Discourse
Scientific Writing :Research Discourse

### Solving Systems of Linear Equations Graphically

• 1. PROPERTIES OF STRAIGHT LINES A. WRITING EQUATION OF A LINE : 1. GIVEN TWO POINTS. 2. GIVEN THE SLOPE AND A POINT B. PARALLEL AND PERPENDICULAR LINES.
• 2. Writing Equations of Lines Equations of lines come in several different forms. Two of those are: 2. Slope-intercept form y = mx + b where m is the slope and b is the y-intercept 2. General form Ax + By + C = 0 Answers will be written in either of these two forms only
• 3. Writing Equations of Lines A. Given a Point and a Slope Find the equation of the line that goes through the point (4, 5) and has a slope of 2. Solution: m = 2 x1 = 4 y1 = 5 y − y1 = m( x − x1 ) Substitute the above given to point- slope form equation a of line. y − 5 = 2( x − 4) Simplify
• 4. Slope-intercept form General Form y − 5 = 2( x − 4) y − 5 = 2( x − 4) y = 2x − 8 + 5 y − 5 = 2x − 8 y = 2x − 3 −2 x + y + 3 = 0 2x − y − 3 = 0 FINAL ANSWER
• 5. Find the equation of the line that goes through the point (-3, 2) and has a slope of -4/5. Solution: m = -4/5 x1 = -3 y1 = 2 y − y1 = m( x − x1 ) Substitute the above given to point- slope form equation a of line. 4 y − 2 = − ( x − −3) 5
• 6. Slope-intercept form General Form 4 4 2 y − 2 = − [ x − (−3)] y = − x− 5 5 5 4 5 y = −4 x − 2 y − 2 = − ( x + 3) 5 4 12 4x + 5 y + 2 = 0 y−2= − x− 5 5 4 2 y = − x− 5 5 FINAL ANSWER
• 7. Writing Equations of Lines B. Given Two Points Find the equation of the line that passes through the points (-2, 3) and (1, -6). Solution: x1 = -2 y1 = 3 x2 = 1 y2 = -6 y2 − y1 Substitute the above given to slope m= formula to find the slope. x2 − x1 −6 − 3 −9 m= m= m = −3 1+ 2 3
• 8. Slope-intercept form General Form y − y1 = m( x − x1 ) y = −3x − 3 y − 3 = −3[ x − (−2)] y − 3 = −3( x + 2) 3x + y + 3 = 0 y − 3 = −3x − 6 y = −3x − 3 FINAL ANSWER
• 9. Definitions Perpendicular Two lines that makes a 90° angle. Lines The slopes of perpendicular lines are negative reciprocal of each other . Parallel Lines Lines that never meet . The slopes of parallel lines are the same.
• 10. Writing Equations of Lines • Given a point and equation of a line parallel to it. A Find the equation of the line that passes through (1, -5) and is parallel to 4x – 2y =3. Solution: x1 = 1 y1 = -5 4x - 2y =3. Rewrite the equation to slope- intercept form to get the slope. - 2y =-4x +3. -4 3 3 y= x+ . y =2x - . m=2 -2 -2 2
• 11. Slope-intercept form General Form y − y1 = m( x − x1 ) y = 2x − 7 y − (−5) = 2( x − 1) y + 5 = 2x − 2 2x − y − 7 = 0 y = 2x − 2 − 5 y = 2x − 7 FINAL ANSWER
• 12. Writing Equations of Lines • Given a point and equation of a line perpendicular to it. B Find the equation of the line that passes through (1, -5) and is perpendicular to 4x – 2y =3. Solution: x1 = 1 y1 = -5 4x - 2y =3. Rewrite the equation to slope- intercept form to get the slope. - 2y =-4x +3. -4 3 3 y= x+ . y =2x - . m=2 -2 -2 2 m = -½
• 13. Slope-intercept form General Form y − y1 = m( x − x1 ) 1 9 y = − x− 2 2 1 y − (−5) = − ( x − 1) 2 2y = −x − 9 1 1 x + 2y + 9 = 0 y+5= − x+ 2 2 1 9 y = − x− 2 2 FINAL ANSWER
• 14. LINEAR EQUATION WITH TWO VARIABLES SOLVING SYSTEM OF EQUATION BY: 2.Graph 3.Substitution 4.Elimination 5.Cramer’s Rule
• 15. Solving Systems of Linear Equations For two-variable systems, there are then three possible types of solutions: Properties A. Independent system: one solution and 1. two distinct non-parallel lines one intersection point 2. cross at exactly one point 3. "independent" system 4. one solution at (x,y )point.
• 16. Solving Systems of Linear Equations B. Inconsistent system: Properties no solution and no intersection point. 1. two distinct parallel lines 2. never cross 3. No point of intersection 4. "inconsistent" system 5. no solution.
• 17. Solving Systems of Linear Equations Properties C. Dependent system: infinitely many solution 1. only one line. 2. same line drawn twice. 3. "intersect" at every point 4. "dependent" system, 5. Infinitely many solutions.
• 18. Methods of Solving Systems of Linear Equations
• 19. A. Systems of Linear Equations: Solving by Graphing Solve the following system by graphing. 2x – 3y = –2 4x + y = 24 Solve for y for each equation Equation 1 Equation 2 2x – 3y = –2 2x + 2 = 3y 4x + y = 24 y = (2/3)x + (2/3) y = –4x + 24
• 20. Get the ( x, y) values for both equation to facilitate easy graphing. The table below shows it x y = (2/3)x + (2/3) y = –4x + 24 –4 –8/3 + 2/3 = –6/3 = –2 16 + 24 = 40 –1 –2/3 + 2/3 = 0 4 + 24 = 28 2 4/3 + 2/3 = 6/3 = 2 –8 + 24 = 16 5 10/3 + 2/3 = 12/3 = 4 –20 + 24 = 4 8 16/3 + 2/3 = 18/3 = 6 –32 + 24 = –8
• 21. Using the table of values we can now graph and look for the intersection: y= (2/3 )x + (2/3 24 x+ solution: (x, y) = (5, 4) ) –4 y=
• 22. B. Systems of Linear Equations: Solving by Substitution Solve the following system by substitution. 2x – 3y = –2 4x + y = 24 Solution: 4x + y = 24 solve the second equation for y: y = –4x + 24 2x – 3(–4x + 24) = –2 substitute it for "y" in 2x + 12x – 72 = –2 the first equation 14x = 70 x=5 solve for x
• 23. Equation 1 Equation 2 x=5 x=5 4x + y = 24 plug this x-value back 2x – 3y = –2 into either equation, 4( 5 ) + y = 24 and solve for y 2( 5 ) – 3y = –2 20 + y = 24 10 – 3y = –2 y = 24 - 20 - 3y = –2 - 10 - 3y = - 12 y=4 y=4 Then the solution is ( x, y ) = (5, 4).
• 24. C. Systems of Linear Equations: Solving by Elimination Solve the following system using elimination. 2x + y = 9 3x – y = 16 Solution: 2x + y = 9 add down, the y's will cancel out 3x – y = 16 5x = 25 x=5 divide through to solve for x
• 25. Equation 1 Equation 2 x=5 x=5 2x + y = 9 using either of the 3x – y = 16 original equations, to 2( 5 ) + y = 9 find the value 3( 5 ) – y = 16 10 + y = 9 of y 15 – y = 16 y = 9 - 10 - y = 16 - 15 -y= 1 y = -1 y = -1 Then the solution is ( x, y ) = (5, -1).
• 26. D. Systems of Linear Equations: Solving by Cramer’s Rule Solve the following system using cramer’s rule. 2x – 3y = –2 4x + y = 24 Solution: Nx Ny x= ,y= D D D - determinant of the coefficient of the variables Nx - determinant taken from D replacing the coefficient of x Ny - and y by their corresponding constant terms leaving all other terms unchanged
• 27. 2 −3 D= D = (2) −( −12) =14 4 1 −2 −3 N x = (−2) − (−72) = 70 Nx = N x 70 24 1 x= = =5 D 14 N y = (48) − (−8) = 56 2 −2 Ny = Ny 56 4 24 y= = =4 D 14 FINAL ( 5, 4 ) ANSWER
• 28. ANSWER THE FOLLOWING PROBLEMS 1. (a) Explain why the simultaneous equations 8x – 4y = 20 and y =2x – 3 have no solution . What can you say about the straight lines representing these two equations? They are parallel • The diagram shows the graph of 2y = x - 2. The values of a and b are respectively. 2 and -1
• 29. The graphs of x - 2y - 3 = 0 and 6 + 4y - 2x = 0 are identical lines • Find the graph of y = -2x - 1? 5. The diagram shows the graph of y = ax + b. Find the values of a and b. a = 2, b = 2
• 30. Find the solution for each system of equation using any method: 1. 5x – 2y = 0 3. y=x+3 4x + y = 13 5y + 6x = 15 Solution : Solution : ( x , y) = ( 2, 5 ) ( x , y) = ( 0, 3 ) 2. 5y = 6x – 3 4. 1 1 x + y =1 2y = x – 4 3 3 1 Solution : y =1 − x ( x , y) = ( -2, -3 ) 2 Solution : ( x , y) = ( -1, 4 )
Aktuelle SpracheEnglish
Español
Portugues
Français
Deutsche