Question

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Question
Select the pair of (x, y) values that makes the following system of equations true:

y=6x−5

y=−x+9
(1 point)
Responses

(1, 8)
(1, 8)

(45,−15)
open paren 4 fifths comma negative 1 fifth close paren

(2, 7)
(2, 7)

(1, 1)
(1, 1)
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Answer 1

To find the correct pair of (x, y) values that satisfy both equations, we can substitute the x-values from the response options into each equation and check if both yield the same y-value.

Let's evaluate each response:

1. **(1, 8)**:
- For \( y = 6x - 5 \):
- \( y = 6(1) - 5 = 6 - 5 = 1 \) (not 8)
- For \( y = -x + 9 \):
- \( y = -1 + 9 = 8 \)

This pair does not satisfy both equations.

2. **(4/5, -1/5)**:
- For \( y = 6x - 5 \):
- \( y = 6(4/5) - 5 = 24/5 - 5 = 24/5 - 25/5 = -1/5 \)
- For \( y = -x + 9 \):
- \( y = -(4/5) + 9 = -4/5 + 45/5 = 41/5 \)

This pair does not satisfy both equations.

3. **(2, 7)**:
- For \( y = 6x - 5 \):
- \( y = 6(2) - 5 = 12 - 5 = 7 \)
- For \( y = -x + 9 \):
- \( y = -2 + 9 = 7 \)

This pair satisfies both equations.

4. **(1, 1)**:
- For \( y = 6x - 5 \):
- \( y = 6(1) - 5 = 6 - 5 = 1 \)
- For \( y = -x + 9 \):
- \( y = -1 + 9 = 8 \)

This pair does not satisfy both equations.

The only pair that makes both equations true is **(2, 7)**.