The solution to the system below is \( (1,-3) \). \( 2 y+x=-5 \) and \( y-3 x=-6 \)

Solve the system of equations \( 2y+x=-5;y-3x=-6 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2y+x=-5\\y-3x=-6\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=-5-2y\\y-3x=-6\end{array}\right.\) - step2: Substitute the value of \(x:\) \(y-3\left(-5-2y\right)=-6\) - step3: Simplify: \(7y+15=-6\) - step4: Move the constant to the right side: \(7y=-6-15\) - step5: Subtract the numbers: \(7y=-21\) - step6: Divide both sides: \(\frac{7y}{7}=\frac{-21}{7}\) - step7: Divide the numbers: \(y=-3\) - step8: Substitute the value of \(y:\) \(x=-5-2\left(-3\right)\) - step9: Simplify: \(x=1\) - step10: Calculate: \(\left\{ \begin{array}{l}x=1\\y=-3\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=1\\y=-3\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(1,-3\right)\) The solution to the system of equations is \( (1,-3) \), which means that the values of \( x \) and \( y \) that satisfy both equations are \( x = 1 \) and \( y = -3 \).