# Spectrum Math Grade 8 Chapter 3 Lesson 8 Answer Key Graphing Linear Equation System

Students can use the Spectrum Math Grade 8 Answer Key Chapter 3 Lesson 3.8 Graphing Linear Equation SystemÂ as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 3 Lesson 3.8 Graphing Linear Equation System Answers Key

Graphing both lines that make up an equation system can solve the system.
y = 3x + 2
y = 2x + 1
Step 1: Graph the first line in the system using slope intercept form as a guide.

Step 2: Graph the second line in the system using slope-intercept form as a guide.
Step 3: Find the point of intersection to solve the equation system.
(-1,-1)

Use slope-intercept form to graph each system of equations and solve the system.

Question 1.
a.
y = -x + 4
y = 3x
x: ____;
y: ____

y: 3
y = -x + 4
y = 3x

Step 1: Graph the first line in the system using slope intercept form as a guide.
Step 2: Graph the second line in the system using slope-intercept form as a guide.
Step 3: Find the point of intersection to solve the equation system.
(1,3)
Therefore, x: 1;
y: 3

b.
y = 2x + 4
y = 3x + 2
x: ____;
y: ____

y: 8
y = 2x + 4
y = 3x + 2

Step 1: Graph the first line in the system using slope intercept form as a guide.
Step 2: Graph the second line in the system using slope-intercept form as a guide.
Step 3: Find the point of intersection to solve the equation system.
(2,8)
Therefore, x: 2;
y: 8

Question 2.
a.
y = -2x – 4
y = -4
x: ____;
y: ____

y:-4
y = -2x – 4
y = -4

Step 1: Graph the first line in the system using slope intercept form as a guide.
Step 2: Graph the second line in the system using slope-intercept form as a guide.
Step 3: Find the point of intersection to solve the equation system.
(0,-4)
Therefore, x: 0;
y:-4

b.
y = 2x – 2
y = -x – 5
x: ____;
y: ____

y:-4
y = 2x – 2
y = -x – 5

Step 1: Graph the first line in the system using slope intercept form as a guide.
Step 2: Graph the second line in the system using slope-intercept form as a guide.
Step 3: Find the point of intersection to solve the equation system.
(-1,-4)
Therefore, x: -1;
y:-4

In some cases, you must first isolate the y before you can solve the system.
2x – 4y = 10
x + y = 2
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = $$\frac{1}{2}$$x – 2$$\frac{1}{2}$$
y = -x + 2

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(3,-1)

Use slope-intercept form to graph each system of equations and solve the system.

Question 1.
a. x + y = 2
-9x + 4y = 8
x: _____;
y: _____

y: 2
x + y = 2
-9x + 4y = 8
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = 2-x
y = 4 + $$\frac{9}{4}$$x

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(0,2)
x: 0;
y: 2

b. 5x + y = 9
10x – 7y = -18
x: _____;
y: _____

y: 4
5x + y = 9
10x – 7y = -18
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = 9-5x
y = $$\frac{18}{7}$$+ $$\frac{10}{7}$$x

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(1,4)
x: 1;
y: 4

Question 2.
a.
2x – y = 0
x + y = -6
x: _____;
y: _____

y: -4
2x – y = 0
x + y = -6
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = 2x
y = -6-x

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(-2,-4)
x: -2;
y: -4

b.
x – 3y = 2
2x + 5y = 15
x: _____;
y: _____

y: 1
x – 3y = 2
2x + 5y = 15
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = $$\frac{1}{3}$$x – $$\frac{2}{3}$$
y = 3 – $$\frac{2}{5}$$x

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(5,1)
x: 5;
y: 1

Use slope-intercept form to graph each system of equations and solve the system.

Question 1.
a.
-2x + 3y = -15
y = -x + 10
x: _____;
y: _____

y: 1
-2x + 3y = -15
y = -x + 10
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = -5 + $$\frac{2}{3}$$x
y = -x + 10

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(9,1)
x: 9;
y: 1

b.
3x + 2y = 9
y = 4x – 1
x: _____;
y: _____

y: 3
3x + 2y = 9
y = 4x – 1
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = $$\frac{9}{2}$$ – $$\frac{3}{2}$$
y = 4x – 1

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(1,3)
x: 1;
y: 3

Question 2.
a.
5x – 2y = 4
y = 2x – 1
x: _____;
y: _____

y: 3
5x – 2y = 4
y = 2x – 1
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = $$\frac{5}{2}$$x – 2
y = 2x – 1

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(2,3)
x: 2;
y: 3

b.
y = -2x – 4
4x – 2y = -8
x: _____;
y: _____

y: 0
y = -2x – 4
4x – 2y = -8
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = -2x – 4
y = 2x + 4

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(-2,0)
x: -2;
y: 0

Question 3.
a.
2y – 4x = 2
y = x + 4
x: _____;
y: _____

y: 7
2y – 4x = 2
y = x + 4
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = 1 + 2x
y = x + 4

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(3,7)
x: 3;
y: 7

b.
x + y = 6
-3x + y = 2
x: _____;
y: _____

y: 5
x + y = 6
-3x + y = 2
Step 1: Isolate y in both equations by using inverse operations to create slope-intercept form.
y = 6 – x
y = 2 + 3x

Step 2: Graph the first, line in the system using slope intercept form as a guide.
Step 3: Graph the second line in the system using slope-intercept form as a guide.
Step 4: Find the point of intersection to solve the equation system.
(1,5)
x: 1;
y: 5

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