Question

Is (−2,2) a viable solution for the following system? Explain. −7x+2y=18 3x+3y=0 (1 point)

Answer 1

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

1. **First equation:**
\(-7x + 2y = 18\)

Substitute \(x = -2\) and \(y = 2\):
\[
-7(-2) + 2(2) = 18
\]
\[
14 + 4 = 18
\]
\[
18 = 18 \quad \text{(true)}
\]

2. **Second equation:**
\(3x + 3y = 0\)

Substitute \(x = -2\) and \(y = 2\):
\[
3(-2) + 3(2) = 0
\]
\[
-6 + 6 = 0
\]
\[
0 = 0 \quad \text{(true)}
\]

Since both equations are satisfied with the substitution of \((-2, 2)\), we can conclude that \((-2, 2)\) is indeed a viable solution for the given system of equations.