Question
Is -2, 2 a viable solution to negative 7x + 2y = 18 and 3x + 3y = 0
Answers
Answered by
GPT-4o mini
To determine if the point \((-2, 2)\) is a solution to the equations \(-7x + 2y = 18\) and \(3x + 3y = 0\), we will substitute \(x = -2\) and \(y = 2\) into both equations and check if they hold true.
**First Equation: \(-7x + 2y = 18\)**
Substituting in the values:
\[
-7(-2) + 2(2) = 18
\]
Calculating:
\[
14 + 4 = 18
\]
\[
18 = 18 \quad \text{(True)}
\]
**Second Equation: \(3x + 3y = 0\)**
Substituting in the values:
\[
3(-2) + 3(2) = 0
\]
Calculating:
\[
-6 + 6 = 0
\]
\[
0 = 0 \quad \text{(True)}
\]
Since both equations are satisfied by the point \((-2, 2)\), we conclude that \((-2, 2)\) is indeed a viable solution to both equations.
**First Equation: \(-7x + 2y = 18\)**
Substituting in the values:
\[
-7(-2) + 2(2) = 18
\]
Calculating:
\[
14 + 4 = 18
\]
\[
18 = 18 \quad \text{(True)}
\]
**Second Equation: \(3x + 3y = 0\)**
Substituting in the values:
\[
3(-2) + 3(2) = 0
\]
Calculating:
\[
-6 + 6 = 0
\]
\[
0 = 0 \quad \text{(True)}
\]
Since both equations are satisfied by the point \((-2, 2)\), we conclude that \((-2, 2)\) is indeed a viable solution to both equations.