Solve the system using elimination. \[ \begin{array}{l}2 x+3 y=-2 \\ 3 x-6 y=18 \\ ([?], \square)\end{array} \]

Solve the system of equations \( 2x+3y=-2;3x-6y=18 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x+3y=-2\\3x-6y=18\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=-\frac{2+3y}{2}\\3x-6y=18\end{array}\right.\) - step2: Substitute the value of \(x:\) \(3\left(-\frac{2+3y}{2}\right)-6y=18\) - step3: Multiply the terms: \(-\frac{3\left(2+3y\right)}{2}-6y=18\) - step4: Multiply both sides of the equation by LCD: \(\left(-\frac{3\left(2+3y\right)}{2}-6y\right)\times 2=18\times 2\) - step5: Simplify the equation: \(-6-21y=36\) - step6: Move the constant to the right side: \(-21y=36+6\) - step7: Add the numbers: \(-21y=42\) - step8: Change the signs: \(21y=-42\) - step9: Divide both sides: \(\frac{21y}{21}=\frac{-42}{21}\) - step10: Divide the numbers: \(y=-2\) - step11: Substitute the value of \(y:\) \(x=-\frac{2+3\left(-2\right)}{2}\) - step12: Simplify: \(x=2\) - step13: Calculate: \(\left\{ \begin{array}{l}x=2\\y=-2\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=2\\y=-2\end{array}\right.\) - step15: Rewrite: \(\left(x,y\right) = \left(2,-2\right)\) The solution to the system of equations using the elimination method is \( (x, y) = (2, -2) \).