Is (−2,2)

Question

a viable solution for the following system? Explain.

−7x+2y=18

3x+3y=0

(1 point)
Responses

(−2,2)
is a nonviable solution since it makes neither equation true.
left parenthesis negative 2 comma 2 right parenthesis is a nonviable solution since it makes neither equation true.

(−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 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 one equation true.

Answer 1

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

1. The first equation is: \[ -7x + 2y = 18 \] Substituting \(x = -2\) and \(y = 2\): \[ -7(-2) + 2(2) = 14 + 4 = 18 \] This is true.

2. The second equation is: \[ 3x + 3y = 0 \] Again substituting \(x = -2\) and \(y = 2\): \[ 3(-2) + 3(2) = -6 + 6 = 0 \] This is also true.

Since \((-2, 2)\) makes both equations true, we can conclude that \((-2, 2)\) is a viable solution.

The correct response is: \((-2, 2)\) is a viable solution since it makes both equations true.