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Question

Solving Equations Using Substitution Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
2 of 52 of 5 Items

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: \[ (-2, 2) \]