Question

What is the solution to the system of equations? -2x + y = -5 3x – 2y = 12 Responses A (3, 1)(3, 1) B (6, 3)(6, 3) C (-2, -9)(-2, -9) D (-2, -1)(-2, -1) E no solutionno solution

Answer 1

To solve this system of equations, we can use either substitution or elimination method.

Let's use the elimination method:

Given equations:
-2x + y = -5 (1)
3x - 2y = 12 (2)

To eliminate y, let's multiply equation (1) by 2 and add it to equation (2):
-4x + 2y = -10
+
3x - 2y = 12

-x = 2
x = -2

Now substitute x = -2 into equation (1):
-2(-2) + y = -5
4 + y = -5
y = -9

Therefore, the solution to the system of equations is (-2, -9), which corresponds to answer choice C.