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Given the equations \begin{align} x_2 + 2x_3 − x_4 + 2x_5 &= 11\\ x_1 + x_2 − x_5 &= 5\\ 2x_1 + x_2 + 2x_3 + x_4 &= 15\\ \end{align} Through row operations I got the equations

\begin{align} 2x_1+x_2+2x3+x_4&=15\\ x_2-2x_3-x4-2x_5&=-5\\ x_3+x_5&= 4 \end{align} It seems that I will have $3$ free variables but I am not sure how to go about solving the equation in echelon form.

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Hint:

Let $x_4=s$ and $x_5=t$.

Express $x_1,x_2,x_3$ in terms of $s$ and $t$.

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