Question

page 8 of 9
Solving Equations Using Substitution Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
Solve the system of equations.
8x−3y= −22

y=10+4x
(1 point)
(
,
)

Answer 1

To solve the system of equations using substitution, follow these steps:

1. Start with the two equations:
\[
8x - 3y = -22 \quad (1)
\]
\[
y = 10 + 4x \quad (2)
\]

2. Substitute equation (2) into equation (1). This means you will replace \( y \) in equation (1) with \( 10 + 4x \):
\[
8x - 3(10 + 4x) = -22
\]

3. Distribute \(-3\) in the equation:
\[
8x - 30 - 12x = -22
\]

4. Combine like terms:
\[
-4x - 30 = -22
\]

5. Add 30 to both sides:
\[
-4x = 8
\]

6. Divide both sides by \(-4\):
\[
x = -2
\]

7. Now, substitute \( x = -2 \) back into equation (2) to find \( y \):
\[
y = 10 + 4(-2)
\]
\[
y = 10 - 8
\]
\[
y = 2
\]

8. The solution to the system of equations is:
\[
(x, y) = (-2, 2)
\]

So, the final answer is:
\[
(-2, 2)
\]