Question

Which ordered pair is a solution to the system of linear equations Negative 4 x + y = 8 and x minus 5 y = 17?
(–4, –3)
(–4, 3)
(–3, –4)
(–3, 4)

Answer 1

To determine which ordered pair is a solution to the system of equations:

1. \(-4x + y = 8\)
2. \(x - 5y = 17\)

we will test each given ordered pair.

**Testing (–4, –3):**
1. For \(-4x + y = 8\):
\(-4(-4) + (-3) = 16 - 3 = 13\) (not equal to 8)

2. For \(x - 5y = 17\):
\(-4 - 5(-3) = -4 + 15 = 11\) (not equal to 17)

**Testing (–4, 3):**
1. For \(-4x + y = 8\):
\(-4(-4) + 3 = 16 + 3 = 19\) (not equal to 8)

2. For \(x - 5y = 17\):
\(-4 - 5(3) = -4 - 15 = -19\) (not equal to 17)

**Testing (–3, –4):**
1. For \(-4x + y = 8\):
\(-4(-3) + (-4) = 12 - 4 = 8\) (this satisfies the equation)

2. For \(x - 5y = 17\):
\(-3 - 5(-4) = -3 + 20 = 17\) (this satisfies the equation)

Since (–3, –4) satisfies both equations, it is a solution.

**Testing (–3, 4):**
1. For \(-4x + y = 8\):
\(-4(-3) + 4 = 12 + 4 = 16\) (not equal to 8)

2. For \(x - 5y = 17\):
\(-3 - 5(4) = -3 - 20 = -23\) (not equal to 17)

The only pair that satisfies both equations is **(–3, –4)**.