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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 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 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 nonviable solution since it makes neither equation true.

1 answer

To determine whether \((-2, 2)\) is a viable solution for the system of equations:

  1. Substitute \(x = -2\) and \(y = 2\) into each equation:

    • For the first equation:
      \(-7x + 2y = 18\)
      \(-7(-2) + 2(2) = 18\)
      \(14 + 4 = 18\)
      \(18 = 18\) (True)

    • For the second equation:
      \(3x + 3y = 0\)
      \(3(-2) + 3(2) = 0\)
      \(-6 + 6 = 0\)
      \(0 = 0\) (True)

Both equations are satisfied by the point \((-2, 2)\).

  1. Conclusion: Since \((-2, 2)\) makes both equations true, it is a viable solution.

Final Answer:

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