\( \begin{array}{lll}-2 x_{1}+x_{1}-3 & \text { vi } & x_{1}-x_{1}+x_{2}-3 \\ -x_{1}-x_{1}-7 & x_{1}-x_{1}-2 x_{3}-27 \\ 2 x_{1}+2 x_{1}-1 & x_{1}-x_{1}+4 x_{3}-9\end{array} \)

Solve the system of equations by following steps: - step0: Solution: \(\left\{ \begin{array}{l}-2x_{1}+x_{1}-3=0\\-x_{1}-x_{1}-7=0\\2x_{1}+2x_{1}-1=0\\x_{1}-x_{1}+x_{2}-3=0\\x_{1}-x_{1}-2x_{3}-27=0\\x_{1}-x_{1}+4x_{3}-9=0\end{array}\right.\) - step1: Calculate: \(\left\{ \begin{array}{l}-x_{1}-3=0\\-2x_{1}-7=0\\4x_{1}-1=0\\x_{2}-3=0\\-2x_{3}-27=0\\4x_{3}-9=0\end{array}\right.\) - step2: Calculate: \(\left\{ \begin{array}{l}x_{1}=-3\\x_{1}=-\frac{7}{2}\\x_{1}=\frac{1}{4}\\x_{2}=3\\x_{3}=-\frac{27}{2}\\x_{3}=\frac{9}{4}\end{array}\right.\) - step3: Find the intersection: \(\left\{ \begin{array}{l}x_{1} \in \varnothing \\x_{2} \in \varnothing \\x_{3} \in \varnothing \end{array}\right.\) - step4: Rewrite: \((x_{1}, x_{2}, x_{3}) \in \varnothing\) The system of equations provided has no solution. This means that the equations are inconsistent and cannot be satisfied simultaneously. To summarize: - The equations derived from your input lead to a contradiction, indicating that there are no values for \( x_1 \), \( x_2 \), and \( x_3 \) that can satisfy all the equations at the same time. If you have any further questions or need assistance with a different problem, feel free to ask!