Is (−2,2) a viable solution for the following system? Explain.

Question

−7x+2y=18

3x+3y=0

(1 point)
Responses

(−2,2) is a viable solution since it makes one equation true.
left parenthesis negative 2 comma 2 right parenthesis is a viable solution since it makes one equation true.

(−2,2) is a nonviable solution since it makes one equation true.
left parenthesis negative 2 comma 2 right parenthesis is a nonviable solution since it makes one equation true.

(−2,2) is a viable solution since it makes both equations true.
left parenthesis negative 2 comma 2 right parenthesis is a viable solution since it makes both equations true.

(−2,2) is a nonviable solution since it makes neither equation true.

Answer 1

To determine if (−2, 2) is a viable solution for the given system of equations, we need to substitute \( x = -2 \) and \( y = 2 \) into both equations and check if they hold true.

1. For the first equation: \[ -7x + 2y = 18 \] Substituting \( x = -2 \) and \( y = 2 \): \[ -7(-2) + 2(2) = 18 \] This simplifies to: \[ 14 + 4 = 18 \] Which is: \[ 18 = 18 \] Therefore, the first equation is satisfied.

2. For the second equation: \[ 3x + 3y = 0 \] Substituting \( x = -2 \) and \( y = 2 \): \[ 3(-2) + 3(2) = 0 \] This simplifies to: \[ -6 + 6 = 0 \] Which is: \[ 0 = 0 \] Therefore, the second equation is also satisfied.

Since (−2, 2) makes both equations true, the correct response is:

(−2,2) is a viable solution since it makes both equations true.