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

(2, 7)
(2, 7)

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

(1, 1)
(1, 1)

(1, 8)

Answer 1

To solve the given system of equations, we will substitute the values of \( x \) from the provided options into both equations to see which pair yields the same value for \( y \).

The equations are:
1. \( y = 6x - 5 \)
2. \( y = -x + 9 \)

Now let's check each option:

1. **Option (2, 7)**:
- Using the first equation: \( y = 6(2) - 5 = 12 - 5 = 7 \)
- Using the second equation: \( y = -2 + 9 = 7 \)
- Both equations give \( y = 7 \). This pair works.

2. **Option (45, −15)**:
- Using the first equation: \( y = 6(45) - 5 = 270 - 5 = 265 \)
- Using the second equation: \( y = -45 + 9 = -36 \)
- Does not match. This pair does not work.

3. **Option (1, 1)**:
- Using the first equation: \( y = 6(1) - 5 = 6 - 5 = 1 \)
- Using the second equation: \( y = -1 + 9 = 8 \)
- Does not match. This pair does not work.

4. **Option (1, 8)**:
- Using the first equation: \( y = 6(1) - 5 = 6 - 5 = 1 \)
- Using the second equation: \( y = -1 + 9 = 8 \)
- Does not match. This pair does not work.

The only option that satisfies both equations is **(2, 7)**.