1.5.3 Systems of algebraic equations

Problem: Solve the system of equations \[ \left\{\begin{array}{c} x_{1}-2 x_{2}-2 x_{3}+x_{4}=1 \\ 2 x_{1}+2 x_{2}-x_{3}+x_{4}=1 \\ x_{1}-x_{2}+x_{3}-2 x_{4}=2 \end{array} .\right. \]