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 ordered pair that solves the system of linear equations, we will substitute each of the given pairs into the equations to see which one is a valid solution.

1. The equations are:
\[
-5x + y = 26 \quad (1)
\]
\[
2x - 7y = 16 \quad (2)
\]

Now we will test each ordered pair:

**A. (–4, 6)**

Substituting into (1):
\[
-5(-4) + 6 = 20 + 6 = 26 \quad \text{(True)}
\]

Substituting into (2):
\[
2(-4) - 7(6) = -8 - 42 = -50 \quad \text{(False)}
\]

**B. (6, –4)**

Substituting into (1):
\[
-5(6) + (-4) = -30 - 4 = -34 \quad \text{(False)}
\]

**C. (–4, –6)**

Substituting into (1):
\[
-5(-4) + (-6) = 20 - 6 = 14 \quad \text{(False)}
\]

**D. (–6, –4)**

Substituting into (1):
\[
-5(-6) + (-4) = 30 - 4 = 26 \quad \text{(True)}
\]

Substituting into (2):
\[
2(-6) - 7(-4) = -12 + 28 = 16 \quad \text{(True)}
\]

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