Question

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

−7x+2y=18
−
7
𝑥
+
2
𝑦
=
18

3x+3y=0
3
𝑥
+
3
𝑦
=
0

(1 point)
Responses

(−2,2)
(
−
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)
(
−
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)
(
−
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)
(
−
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.

Answer 1

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

### First Equation:

\[
-7x + 2y = 18
\]

Substituting \(x = -2\) and \(y = 2\):

\[
-7(-2) + 2(2) = 18
\]

Calculating:

\[
14 + 4 = 18
\]

This simplifies to:

\[
18 = 18 \quad \text{(True)}
\]

### Second Equation:

\[
3x + 3y = 0
\]

Now substituting \(x = -2\) and \(y = 2\):

\[
3(-2) + 3(2) = 0
\]

Calculating:

\[
-6 + 6 = 0
\]

This simplifies to:

\[
0 = 0 \quad \text{(True)}
\]

### Conclusion:

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

The correct response is:

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