Find the solution to the system of equations. You can use the interactive graph below to find the solution. \( \left\{\begin{array}{l}-2 x+2 y=-4 \\ 3 x+3 y=-18\end{array}\right. \) \( x=\square \)
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The Deep Dive
First, let's simplify the given equations. For the first equation, \(-2x + 2y = -4\), we can divide everything by 2 to get \(y = x - 2\). Now for the second equation, \(3x + 3y = -18\), we can divide by 3, resulting in \(x + y = -6\). Substituting \(y\) from the first simplified equation into the second gives us \(x + (x - 2) = -6\). Solving this, you’ll find that \(2x - 2 = -6\) leads to \(2x = -4\), thus \(x = -2\). Now, looking back to find \(y\), substituting \(-2\) back into \(y = x - 2\) gives \(y = -2 - 2 = -4\). Therefore, the solution to the system of equations is \(x = -2\) and \(y = -4\). To sum it up clearly: \(x = -2\) \(y = -4\)