6) \( \begin{aligned} 6 x+6 y & =-6 \\ -2 x-3 y & =-3\end{aligned} \)

Solve the system of equations \( 6x+6y=-6;-2x-3y=-3 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}6x+6y=-6\\-2x-3y=-3\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=-1-y\\-2x-3y=-3\end{array}\right.\) - step2: Substitute the value of \(x:\) \(-2\left(-1-y\right)-3y=-3\) - step3: Simplify: \(2-y=-3\) - step4: Move the constant to the right side: \(-y=-3-2\) - step5: Subtract the numbers: \(-y=-5\) - step6: Change the signs: \(y=5\) - step7: Substitute the value of \(y:\) \(x=-1-5\) - step8: Simplify: \(x=-6\) - step9: Calculate: \(\left\{ \begin{array}{l}x=-6\\y=5\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=-6\\y=5\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(-6,5\right)\) The solution to the system of equations is \( (x,y) = (-6,5) \).