Question

Which ordered pair is the solution to the system of linear equations Negative 5 x + y = 26 and 2 x minus 7 y = 16?
(–4, 6)
(6, –4)
(–4, –6)
(–6, –4)

Answer 1

To find the solution to the system of linear equations given by:

1. \( -5x + y = 26 \)
2. \( 2x - 7y = 16 \)

we will substitute the ordered pairs into each equation to see which one satisfies both equations.

### Checking the options:

1. **Option (–4, 6)**:
- For the first equation:
\[
-5(-4) + 6 = 20 + 6 = 26 \quad \text{(True)}
\]
- For the second equation:
\[
2(-4) - 7(6) = -8 - 42 = -50 \quad \text{(False)}
\]

2. **Option (6, –4)**:
- For the first equation:
\[
-5(6) + (-4) = -30 - 4 = -34 \quad \text{(False)}
\]

3. **Option (–4, –6)**:
- For the first equation:
\[
-5(-4) + (-6) = 20 - 6 = 14 \quad \text{(False)}
\]

4. **Option (–6, –4)**:
- For the first equation:
\[
-5(-6) + (-4) = 30 - 4 = 26 \quad \text{(True)}
\]
- For the second equation:
\[
2(-6) - 7(-4) = -12 + 28 = 16 \quad \text{(True)}
\]

### Conclusion:
The only ordered pair that satisfies both equations is \((-6, -4)\).

Thus, the solution to the system of linear equations is \((-6, -4)\).