Solve a System of Equations by Graphing

Topics

Uncategorized

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 7

1. Question
Find the solution to the system of equations by graphing.

$x-3=0$

$x+y=1$
- $x=$ (3) $y=$ (-2)
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

First graph the equations.

Graph: $x-3=0$

Make $x$ the subject to get the equation of the line.

$x-3 \ color(crimson)(+3)$ $=$ $0 \ color(crimson)(+3)$ Add $3$ to both sides

$x \ cancel(-3) cancel(+3)$ $=$ $0 \ color(crimson)(+3)$

$x$ $=$ $3$

Graph: $x+y=1$

First, make $y$ the subject.

$x+y$ $=$ $1$

$y$ $=$ $-x+1$ Make $y$ the subject

Working out the y-values for each x-value in the table of values.

$x$ $0$ $1$ $2$ $3$

$y$ $1$ $0$ $-1$ $-2$

Plot the points and draw the graph.

The graphs intersect at the point $(3,-2)$

$:. color(darkviolet)(x=3, \ y=-2)$

$x=3, y=-2$
Question 2 of 7

2. Question
Find the solution to the system of equations by graphing.

$2x+y=5$

$5x-3y=7$
- $x=$ (2) $y=$ (1)
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

First graph the equations.

Graph: $2x+y=5$

Make $y$ the subject to get the equation of the line.

$2x+y \ color(crimson)(-2x)$ $=$ $5 \ color(crimson)(-2x)$ Add $-2x$ to both sides

$y \ cancel(+2x) cancel(-2x)$ $=$ $5 \ color(crimson)(-2x)$

$y$ $=$ $-2x+5$

Working out the y-values for each x-value in the table of values.

$x$ $0$ $1$ $2$ $3$

$y$ $5$ $3$ $1$ $-1$

Plot the points and draw the graph.

Graph: $5x-3y=7$

First, make $y$ the subject.

$5x-3y$ $=$ $7$ Make $y$ the subject

$-3y$ $=$ $-5x+7$ Add $-5x$ to both sides

$y$ $=$ $5/3x-7/3$ Divide both sides by $-3$

Working out the y-values for each x-value in the table of values.

$x$ $0$ $1$ $2$ $3$

$y$ $-7/3$ $-2/3$ $1$ $8/3$

Plot the points and draw the graph.

The graphs intersect at the point $(2,1)$

$:. color(darkviolet)(x=2, \ y=1)$

$x=2, y=1$

Question 3 of 7

Find the solution to the system of equations by graphing.

$4x-3y=1$

$3x+2y=5$

$x=$ (1) $y=$ (1)

Question 4 of 7

Find the solution to the system of equations by graphing.

$x+3y=15$

$y-x=1$

$x=$ (3) $y=$ (4)

Question 5 of 7

5. Question
Find the solution to the system of equations by graphing.

$2x+y=2$

$x+y=2$
- $x=$ (0) $y=$ (2)
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

First graph the equations.

Graph: $2x+y=2$

Make $y$ the subject to get the equation of the line.

$2x+y \ color(crimson)(-2x)$ $=$ $2 \ color(crimson)(-2x)$ Add $-2x$ to both sides

$y \ cancel(+2x) cancel(-2x)$ $=$ $2\ color(crimson)(-2x)$

$y$ $=$ $-2x+2$

Working out the y-values for each x-value in the table of values.

$x$ $0$ $1$ $2$ $3$

$y$ $2$ $0$ $-2$ $-4$

Plot the points and draw the graph.

Graph: $x+y=2$

First, make $y$ the subject.

$x+y$ $=$ $2$

$y$ $=$ $-x+2$ Make $y$ the subject

Working out the y-values for each x-value in the table of values.

$x$ $0$ $1$ $2$ $3$

$y$ $2$ $1$ $0$ $-1$

Plot the points and draw the graph.

The graphs intersect at the point $(0,2)$

$:. color(darkviolet)(x=0, \ y=2)$

$x=0, y=2$
Question 6 of 7

6. Question
Find the solution to the system of equations by graphing.

$y-x=4$

$x-y=1$
- $x=$ (no solution) $y=$ (no solution)
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

First graph the equations.

Graph: $y-x=4$

Make $y$ the subject to get the equation of the line.

$y-x \ color(crimson)(+x)$ $=$ $4 \ color(crimson)(+x)$ Add $x$ to both sides

$y \ cancel(-x) cancel(+x)$ $=$ $4 \ color(crimson)(+x)$

$y$ $=$ $x+4$

Working out the y-values for each x-value in the table of values.

$x$ $-2$ $0$ $2$ $4$

$y$ $2$ $4$ $6$ $8$

Plot the points and draw the graph.

Graph: $x+y=1$

First, make $y$ the subject.

$x-y$ $=$ $1$

$y$ $=$ $x-1$ Make $y$ the subject

Working out the y-values for each x-value in the table of values.

$x$ $-2$ $0$ $2$ $4$

$y$ $-3$ $-1$ $1$ $3$

Plot the points and draw the graph.

The graphs are parallel the lines do not intersect.

There is no solution.

There is no solution.

Question 7 of 7

Find the solution to the system of equations by graphing.

$-6x+2y=8$

$y=3x+4$

$x=$ (infinite solutions) $y=$ (infinite solutions)

$4x-3y \ color(crimson)(-4x)$	$=$	$1 \ color(crimson)(-4x)$	Add $-4x$ to both sides
$-3y \ cancel(+4x) cancel(-4x)$	$=$	$1 \ color(crimson)(-4x)$
$\ color(crimson)(-3)y \ color(crimson)(\div(-3))$	$=$	$(-4x+1 )\ color(crimson)(\div(-3))$	Divide both sides by $-3$
$y$	$=$	$4/3x-1/3$

$x+3y \ color(crimson)(-x)$	$=$	$15 \ color(crimson)(-x)$	Add $-x$ to both sides
$3y \ cancel(+x) cancel(-x)$	$=$	$15 \ color(crimson)(-x)$
$\ color(crimson)(3)y\ color(crimson)(\div(3))$	$=$	$(-x+15) \ color(crimson)(\div(3))$	Divide both sides by $3$
$y$	$=$	$-1/3x+5$

$-6x+2y \ color(crimson)(+6x)$	$=$	$8 \ color(crimson)(+6x)$	Add $6x$ to both sides
$2y \ cancel(-6x) cancel(+6x)$	$=$	$8 \ color(crimson)(+6x)$
$\ color(crimson)(2)y\ color(crimson)(\div(2))$	$=$	$(6x+8) \ color(crimson)(\div(2))$	Divide both sides by $2$
$y$	$=$	$3x+4$

Solve a System of Equations by Graphing

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Great Work!

2. Question

Great Work!

3. Question

Great Work!

4. Question

Great Work!

5. Question

Great Work!

6. Question

Great Work!

7. Question

Great Work!

Quizzes

$x-3 \ color(crimson)(+3)$	$=$	$0 \ color(crimson)(+3)$	Add $3$ to both sides
$x \ cancel(-3) cancel(+3)$	$=$	$0 \ color(crimson)(+3)$
$x$	$=$	$3$

$2x+y \ color(crimson)(-2x)$	$=$	$5 \ color(crimson)(-2x)$	Add $-2x$ to both sides
$y \ cancel(+2x) cancel(-2x)$	$=$	$5 \ color(crimson)(-2x)$
$y$	$=$	$-2x+5$

$5x-3y$	$=$	$7$	Make $y$ the subject
$-3y$	$=$	$-5x+7$	Add $-5x$ to both sides
$y$	$=$	$5/3x-7/3$	Divide both sides by $-3$

$3x+2y$	$=$	$5$	Make $y$ the subject
$2y$	$=$	$-3x+5$	Add $-3x$ to both sides
$y$	$=$	$-3/2x+5/2$	Divide both sides by $2$

$2x+y \ color(crimson)(-2x)$	$=$	$2 \ color(crimson)(-2x)$	Add $-2x$ to both sides
$y \ cancel(+2x) cancel(-2x)$	$=$	$2\ color(crimson)(-2x)$
$y$	$=$	$-2x+2$

$y-x \ color(crimson)(+x)$	$=$	$4 \ color(crimson)(+x)$	Add $x$ to both sides
$y \ cancel(-x) cancel(+x)$	$=$	$4 \ color(crimson)(+x)$
$y$	$=$	$x+4$

$x$	$0$	$1$	$2$	$3$
$y$	$1$	$0$	$-1$	$-2$

$x$	$0$	$1$	$2$	$3$
$y$	$-7/3$	$-2/3$	$1$	$8/3$

$x$	$0$	$1$	$2$	$3$
$y$	$-1/3$	$1$	$7/3$	$11/3$

$x$	$0$	$1$	$2$	$3$
$y$	$5/2$	$1$	$-1/2$	$-2$