We included **HMH Into Math Grade 8 Answer Key**** PDF** **Module 7 Systems of Linear Equations **to make students experts in learning maths.

## HMH Into Math Grade 8 Module 7 Answer Key Systems of Linear Equations

**Wags Per Mile**

Write expressions showing the cost of using each service for d days.

A. Nikki’s: _____

B. Jaden’s: _____

Find when the dog services will cost the same.

C. The dog services cost the same on day _____

A. Nikki’s: (10 + 15) = 25d

B. Jaden’s: (20 + 13)d = 33d

**Turn and Talk**

Describe the steps you used to solve Part C.

**Are You Ready?**

**Complete these problems to review prior concepts and skills you will need for this module.**

**Identify Solutions of Equations**

**Use substitution to determine whether the given value of the variable is a solution of the equation.**

Question 1.

6x – 2x = 10; x = 2

Answer:

6x – 2x = 10

x = 2

4x = 10

4(2) = 10

8 ≠ 10

It is not a solution.

Question 2.

4n + 4 = 14; n = 2.5

Answer:

4n + 4 = 14;

n = 2.5

4n = 14 – 4

4n = 10

4(2.5) = 10

10 = 10

Thus n = 2.5 is a solution.

Question 3.

\(\frac{1}{3}\)a – 1 = \(\frac{1}{4}\)a; a = 12

Answer:

\(\frac{1}{3}\)a – 1 = \(\frac{1}{4}\)a;

a = 12

\(\frac{1}{3}\)a – \(\frac{1}{4}\)a = 1

\(\frac{1}{3}\)(12) – \(\frac{1}{4}\)(12) = 1

4 – 3 = 1

1 = 1

a = 12 is a solution.

Question 4.

\(\frac{3}{4}\)(t – 6) = 9; t = 20

Answer:

\(\frac{3}{4}\)(t – 6) = 9;

t = 20

\(\frac{3}{4}\)(20 – 6) = 9

\(\frac{3}{4}\) (14) = 9

14 × 3 = 9 × 4

42 ≠ 36

It is not a solution.

**Solve Multi-Step Equations**

**Solve each equation.**

Question 5.

3b + 4 = 5b – 8

Answer:

3b + 4 = 5b – 8

3b – 5b = -8 – 4

-2b = -12

b = 6

Question 6.

-2(x + 6) = 4x

Answer:

-2(x + 6) = 4x

-2x – 12 = 4x

-2x – 4x = 12

-6x = 12

x = -12/6

x = -2

Question 7.

\(\frac{1}{4}\)(s + 6) = -3

Answer:

\(\frac{1}{4}\)(s + 6) = -3

\(\frac{1}{4}\)s + \(\frac{6}{4}\) = -3

\(\frac{1}{4}\)s = -3 – \(\frac{3}{2}\)

\(\frac{1}{4}\)s = (-6 – 3)/2

\(\frac{1}{4}\)s = -9/2

s = -9/2 × 4

s = -9 × 2

s = -18

Question 8.

2m + 1.5 = 3m – 11.7

Answer:

2m + 1.5 = 3m – 11.7

2m – 3m = -1.5 – 11.7

-m = -13.2

m = 13.2

**Special Cases of Equations**

**Complete each equation by writing a number in the box so that the equation has the given number of solutions.**

Question 9.

x + 5 = 3(2x + 1); no solution

Answer: 6

Explanation:

3(2x + 1) = 6x + 3

Add 2 on both sides

3(2x + 1) + 2 = 6x + 3 + 2

3(2x + 1) + 2 = 6x + 5

Question 10.

-4n + 8 = 4n – 8n + infinitely many solutions

Answer:

-4n + 8 = 4n – 8n +** 8**

Question 11.

Saskia is solving an equation in one variable and gets the equivalent equation 3 = 3. Assuming her work is correct, what can she conclude about the original equation? Explain.

Answer:

Let us use the equation

x + 3 = x + 3

x = x or 3 = 3

x + 3 = x + 3

x = 2

2 + 3 = 2 + 3

5 = 5

We can see that both sides of the equation are always the same with any value of x.