5. \( \left\{\begin{array}{l}-3 x+y=9 \\ -3 x+2 y=9\end{array}\right. \)

Solve the system of equations \( -3x+y=9;-3x+2y=9 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-3x+y=9\\-3x+2y=9\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=9+3x\\-3x+2y=9\end{array}\right.\) - step2: Substitute the value of \(y:\) \(-3x+2\left(9+3x\right)=9\) - step3: Simplify: \(3x+18=9\) - step4: Move the constant to the right side: \(3x=9-18\) - step5: Subtract the numbers: \(3x=-9\) - step6: Divide both sides: \(\frac{3x}{3}=\frac{-9}{3}\) - step7: Divide the numbers: \(x=-3\) - step8: Substitute the value of \(x:\) \(y=9+3\left(-3\right)\) - step9: Calculate: \(y=0\) - step10: Calculate: \(\left\{ \begin{array}{l}x=-3\\y=0\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=-3\\y=0\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(-3,0\right)\) The solution to the system of equations is \( x = -3 \) and \( y = 0 \).