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 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.**