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.
x=6y−3

2x+7y=13
(1 point)
(
,
)
R

Answer 1

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

1. We have the equations:
\[
x = 6y - 3 \quad \text{(1)}
\]
\[
2x + 7y = 13 \quad \text{(2)}
\]

2. Substitute equation (1) into equation (2) for \(x\):
\[
2(6y - 3) + 7y = 13
\]

3. Distribute the 2:
\[
12y - 6 + 7y = 13
\]

4. Combine like terms:
\[
19y - 6 = 13
\]

5. Add 6 to both sides:
\[
19y = 19
\]

6. Divide by 19:
\[
y = 1
\]

7. Now substitute \(y = 1\) back into equation (1) to find \(x\):
\[
x = 6(1) - 3
\]
\[
x = 6 - 3
\]
\[
x = 3
\]

8. The solution to the system of equations is:
\[
(x, y) = (3, 1)
\]

Thus, the final answer is:
\[
(3, 1)
\]