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 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 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 neither equation true.

Answer 1

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

1. **First equation:**
\(-7x + 2y = 18\)
\[
-7(-2) + 2(2) = 14 + 4 = 18
\]
This equation is true.

2. **Second equation:**
\(3x + 3y = 0\)
\[
3(-2) + 3(2) = -6 + 6 = 0
\]
This equation is also true.

Since the point \((-2, 2)\) satisfies both equations, it is a viable solution.

Therefore, the correct response is:

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