Question

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.
5x+2y=14

x−6y=22
(1 point)

Answer 1

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

1. Start with the two equations:
\[
5x + 2y = 14 \quad (1)
\]
\[
x - 6y = 22 \quad (2)
\]

2. Solve one of the equations for one variable. Let's solve equation (2) for \(x\):
\[
x = 22 + 6y \quad (3)
\]

3. Now substitute equation (3) into equation (1):
\[
5(22 + 6y) + 2y = 14
\]

4. Distribute \(5\):
\[
110 + 30y + 2y = 14
\]
\[
110 + 32y = 14
\]

5. Subtract \(110\) from both sides:
\[
32y = 14 - 110
\]
\[
32y = -96
\]

6. Divide by \(32\):
\[
y = -3
\]

7. Now, substitute \(y = -3\) back into equation (3) to find \(x\):
\[
x = 22 + 6(-3)
\]
\[
x = 22 - 18
\]
\[
x = 4
\]

8. So, the solution to the system of equations is:
\[
(x, y) = (4, -3)
\]

The final answer is:
\[
\boxed{(4, -3)}
\]