We are given a system of two linear equations with two variables, $x$ and $y$: $7x + 5y = 59$ $3x - 9y = 159$ We need to find which of the given ordered pairs (A: (-17, -12), B: (-17, 12), C: (17, -12), D: (17, 12)) is a solution to the system. A solution is an ordered pair $(x, y)$ that satisfies both equations.

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$:

$7x + 5y = 59$

$3x - 9y = 159$

We need to find which of the given ordered pairs (A: (-17, -12), B: (-17, 12), C: (17, -12), D: (17, 12)) is a solution to the system. A solution is an ordered pair $(x, y)$ that satisfies both equations.

2. Solution Steps

We can test each ordered pair by substituting the $x$ and $y$ values into both equations and checking if the equations hold true.

A. (-17, -12):

$7(-17) + 5(-12) = -119 - 60 = -179 \neq 59$

Since the first equation is not satisfied, (-17, -12) is not a solution.

B. (-17, 12):

$7(-17) + 5(12) = -119 + 60 = -59 \neq 59$

Since the first equation is not satisfied, (-17, 12) is not a solution.

C. (17, -12):

$7(17) + 5(-12) = 119 - 60 = 59$

$3(17) - 9(-12) = 51 + 108 = 159$

Both equations are satisfied, so (17, -12) is a solution.

D. (17, 12):

$7(17) + 5(12) = 119 + 60 = 179 \neq 59$

Since the first equation is not satisfied, (17, 12) is not a solution.

3. Final Answer

The ordered pair that is a solution to the system of equations is C. (17, -12).