I am stuck with system of linear equations. I need to put them aligned so that it looks like this:

I wrote a code (but wrong) so you can work with it.
Code: Select all
\begin{align*}
x_0 &+\frac{7}{22}x_3 &+\frac{5}{22}x_4 &= \frac{21}{2}\\
&x_1 &+\frac{3}{22}x_3 &-\frac{1}{22}x_4 &= \frac{7}{2}\\
&x_2 &+\frac{1}{22}x_3 &+\frac{7}{22}x_4 &= \frac{7}{2}\\
&\frac{3}{2}x_3 &+\frac{5}{2}x_4 &+x_5 &= \frac{55}{2}.
\end{align*}