So I have the following problem:
And I have obtained the following system of equations: $\begin{align*} -x_1+x_2&=400\\ x_1+x_3-x_4&=600\\ x_2+x_3+x_5&=300\\ x_4+x_5&=100 \end{align*}$
By using the Gaussian elimination method, I found the following system of equations (using rref() on a TI83):
$\begin{align*} x_1+x_3+x_5&=0\\ x_2+x_3+x_5&=0\\ x_4+x_5&=1\\ 0&=1 \end{align*}$
I would like some clarification as to what I am doing wrong.
Thank you.