Solve the system of equations by substitution. \( \begin{array}{l}-3 x-2 y-z=-1 \\ 2 x+y+3 z=-10 \\ y=-3\end{array} \)

Solve the system of equations \( -3x-2y-z=-1;2x+y+3z=-10;y=-3 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-3x-2y-z=-1\\2x+y+3z=-10\\y=-3\end{array}\right.\) - step1: Substitute the value of \(y:\) \(\left\{ \begin{array}{l}-3x-2\left(-3\right)-z=-1\\2x-3+3z=-10\end{array}\right.\) - step2: Simplify: \(\left\{ \begin{array}{l}-3x+6-z=-1\\2x-3+3z=-10\end{array}\right.\) - step3: Solve the equation: \(\left\{ \begin{array}{l}z=7-3x\\2x-3+3z=-10\end{array}\right.\) - step4: Substitute the value of \(z:\) \(2x-3+3\left(7-3x\right)=-10\) - step5: Simplify: \(-7x+18=-10\) - step6: Move the constant to the right side: \(-7x=-10-18\) - step7: Subtract the numbers: \(-7x=-28\) - step8: Change the signs: \(7x=28\) - step9: Divide both sides: \(\frac{7x}{7}=\frac{28}{7}\) - step10: Divide the numbers: \(x=4\) - step11: Substitute the value of \(x:\) \(z=7-3\times 4\) - step12: Simplify: \(z=-5\) - step13: Calculate: \(\left\{ \begin{array}{l}x=4\\y=-3\\z=-5\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=4\\y=-3\\z=-5\end{array}\right.\) - step15: Rewrite: \(\left(x,y,z\right) = \left(4,-3,-5\right)\) The solution to the system of equations by substitution is \( (x,y,z) = (4,-3,-5) \).