\( \rightarrow \begin{array} { r } { - 2 x - 3 y + z = - 9 } \\ { - 2 x + y - 3 z = 7 } \\ { x - y + 2 z = - 5 } \end{array} \} \)

Solve the system of equations \( -2x-3y+z=-9;-2x+y-3z=7;x-y+2z=-5 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-2x-3y+z=-9\\-2x+y-3z=7\\x-y+2z=-5\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}z=-9+2x+3y\\-2x+y-3z=7\\x-y+2z=-5\end{array}\right.\) - step2: Substitute the value of \(z:\) \(\left\{ \begin{array}{l}-2x+y-3\left(-9+2x+3y\right)=7\\x-y+2\left(-9+2x+3y\right)=-5\end{array}\right.\) - step3: Simplify: \(\left\{ \begin{array}{l}-8x-8y+27=7\\5x+5y-18=-5\end{array}\right.\) - step4: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{5-2y}{2}\\5x+5y-18=-5\end{array}\right.\) - step5: Substitute the value of \(x:\) \(5\times \frac{5-2y}{2}+5y-18=-5\) - step6: Simplify: \(\frac{5\left(5-2y\right)}{2}+5y-18=-5\) - step7: Multiply both sides of the equation by LCD: \(\left(\frac{5\left(5-2y\right)}{2}+5y-18\right)\times 2=-5\times 2\) - step8: Simplify the equation: \(-11=-10\) - step9: The statement is false: \(y \in \varnothing \) - step10: Calculate: \(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \\z \in \varnothing \end{array}\right.\) - step11: Rewrite: \((x, y, z) \in \varnothing\) The system of equations has no solution.