Question

Is (−2,2)
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.**