12) \( \begin{aligned}-7 x+y & =-19 \\ -2 x+3 y & =-19\end{aligned} \)

Solve the system of equations \( -7x+y=-19;-2x+3y=-19 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-7x+y=-19\\-2x+3y=-19\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=-19+7x\\-2x+3y=-19\end{array}\right.\) - step2: Substitute the value of \(y:\) \(-2x+3\left(-19+7x\right)=-19\) - step3: Simplify: \(19x-57=-19\) - step4: Move the constant to the right side: \(19x=-19+57\) - step5: Add the numbers: \(19x=38\) - step6: Divide both sides: \(\frac{19x}{19}=\frac{38}{19}\) - step7: Divide the numbers: \(x=2\) - step8: Substitute the value of \(x:\) \(y=-19+7\times 2\) - step9: Calculate: \(y=-5\) - step10: Calculate: \(\left\{ \begin{array}{l}x=2\\y=-5\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=2\\y=-5\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(2,-5\right)\) The solution to the system of equations is \( x = 2 \) and \( y = -5 \).