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Question

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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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).