Is (−2,2)

Question

(
−
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.