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Question
Solve the system of equations below using substitution.

x+y=34
6x−y=15
(1 point)
Responses

(7,27)
(7,27)

(-60.5, 94.5)
(-60.5, 94.5)

(7, 42)
(7, 42)

(27, 7)
(27, 7)
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page 5 of 5

Answer 1

To solve the system of equations using substitution:

1. The given equations are:
\[
x + y = 34 \quad \text{(1)}
\]
\[
6x - y = 15 \quad \text{(2)}
\]

2. Start by solving equation (1) for \(y\):
\[
y = 34 - x
\]

3. Substitute this expression for \(y\) into equation (2):
\[
6x - (34 - x) = 15
\]

4. Simplify the equation:
\[
6x - 34 + x = 15
\]
\[
7x - 34 = 15
\]

5. Add 34 to both sides:
\[
7x = 49
\]

6. Divide by 7:
\[
x = 7
\]

7. Now substitute \(x = 7\) back into the equation for \(y\):
\[
y = 34 - 7 = 27
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (7, 27)
\]

The correct response is **(7, 27)**.