20) \( \begin{array}{l}2 x+3 y=-12 \\ 5 x-3 y=-9\end{array} \)

Solve the system of equations \( 2x+3y=-12;5x-3y=-9 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x+3y=-12\\5x-3y=-9\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=-\frac{12+3y}{2}\\5x-3y=-9\end{array}\right.\) - step2: Substitute the value of \(x:\) \(5\left(-\frac{12+3y}{2}\right)-3y=-9\) - step3: Multiply the terms: \(-\frac{5\left(12+3y\right)}{2}-3y=-9\) - step4: Multiply both sides of the equation by LCD: \(\left(-\frac{5\left(12+3y\right)}{2}-3y\right)\times 2=-9\times 2\) - step5: Simplify the equation: \(-60-21y=-18\) - step6: Move the constant to the right side: \(-21y=-18+60\) - 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 \(y:\) \(x=-\frac{12+3\left(-2\right)}{2}\) - step12: Simplify: \(x=-3\) - step13: Calculate: \(\left\{ \begin{array}{l}x=-3\\y=-2\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=-3\\y=-2\end{array}\right.\) - step15: Rewrite: \(\left(x,y\right) = \left(-3,-2\right)\) The solution to the system of equations is \( x = -3 \) and \( y = -2 \).