Use technology to solve the system of equations, if a solution exists. (If there are infinitely ma $$ \begin{array}{l} x_{1}+2 x_{2}-x_{3}+x_{4}=4 \ x_{1}+3 x_{2}+4 x_{3}+x_{4}=-4 \ 2 x_{1}+5 x_{2}+2 x_{3}+2 x_{4}= 1 \ 2 x_{1}+3 x_{2}-6 x_{3}+2 x_{4}=4\end{array} $$ $$ \left(x_{1}, x_{2}, x_{3}, x_{4}\right)=(\square) $$

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Solve the system of equations $$ x_{1}+2 x_{2}-x_{3}+x_{4}=4;x_{1}+3 x_{2}+4 x_{3}+x_{4}=-4;2 x_{1}+5 x_{2}+2 x_{3}+2 x_{4}=1;2 x_{1}+3 x_{2}-6 x_{3}+2 x_{4}=4 $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}x_{1}+2x_{2}-x_{3}+x_{4}=4\x_{1}+3x_{2}+4x_{3}+x_{4}=-4\2x_{1}+5x_{2}+2x_{3}+2x_{4}=1\2x_{1}+3x_{2}-6x_{3}+2x_{4}=4\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x_{1}=4-2x_{2}+x_{3}-x_{4}\x_{1}+3x_{2}+4x_{3}+x_{4}=-4\2x_{1}+5x_{2}+2x_{3}+2x_{4}=1\2x_{1}+3x_{2}-6x_{3}+2x_{4}=4\end{array}ight.$$
- step2: Substitute the value of $$x_{1}:$$
  $$\left\{ \begin{array}{l}4-2x_{2}+x_{3}-x_{4}+3x_{2}+4x_{3}+x_{4}=-4\2\left(4-2x_{2}+x_{3}-x_{4}ight)+5x_{2}+2x_{3}+2x_{4}=1\2\left(4-2x_{2}+x_{3}-x_{4}ight)+3x_{2}-6x_{3}+2x_{4}=4\end{array}ight.$$
- step3: Simplify:
  $$\left\{ \begin{array}{l}4+x_{2}+5x_{3}=-4\8+x_{2}+4x_{3}=1\8-x_{2}-4x_{3}=4\end{array}ight.$$
- step4: Solve the equation:
  $$\left\{ \begin{array}{l}x_{2}=-8-5x_{3}\8+x_{2}+4x_{3}=1\8-x_{2}-4x_{3}=4\end{array}ight.$$
- step5: Substitute the value of $$x_{2}:$$
  $$\left\{ \begin{array}{l}8-8-5x_{3}+4x_{3}=1\8-\left(-8-5x_{3}ight)-4x_{3}=4\end{array}ight.$$
- step6: Simplify:
  $$\left\{ \begin{array}{l}-x_{3}=1\16+x_{3}=4\end{array}ight.$$
- step7: Solve the equation:
  $$\left\{ \begin{array}{l}x_{3}=-1\16+x_{3}=4\end{array}ight.$$
- step8: Substitute the value of $$x_{3}:$$
  $$16-1=4$$
- step9: Simplify:
  $$15=4$$
- step10: Calculate:
  $$\left\{ \begin{array}{l}x_{1} \in \varnothing \x_{2} \in \varnothing \x_{3} \in \varnothing \x_{4} \in \varnothing \end{array}ight.$$
- step11: Rewrite:
  $$(x_{1}, x_{2}, x_{3}, x_{4}) \in \varnothing$$
The system of equations does not have a solution.
The system of equations has no solution.

Use technology to solve the system of equations, if a solution exists. (If there are infinitely ma

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