Students can use the **Spectrum Math Grade 8 Answer Key** **Chapter 3 Lesson 3.8 Graphing Linear Equation System** 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: ____

Answer: x: 1;

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: ____

Answer: x: 2;

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: ____

Answer: x: 0;

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: ____

Answer: x: -1;

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: _____

Answer: x: 0;

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: _____

Answer: x: 1;

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: _____

Answer: x: -2;

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: _____

Answer: x: 5;

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: _____

Answer: x: 9;

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: _____

Answer: x: 1;

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: _____

Answer: x: 2;

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: _____

Answer: x: -2;

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: _____

Answer: x: 3;

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: _____

Answer: x: 1;

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