Answer
$$x=100-3s+96t, \quad y=s, \quad z=54+52t, \quad w=t.$$
Work Step by Step
The augmented matrix is given by
$$\left[ \begin {array}{ccccc} 4&12&-7&-20&22\\ 3&9&-
5&-28&30\end {array} \right].
$$
Multiply the first row by $-3$ and adding it to $4$ times the second row , we get
$$\left[ \begin {array}{ccccc} 4&12&-7&-20&22\\ 0&0&
1&-42&54\end {array} \right].
$$
Now, the crossposting system is given by
$$
\begin{align*}
4x+12y-7z-20w&=22 \\
z-52w&=54.
\end{align*}
$$
The above system has the solution
$$x=100-3s+96t, \quad y=s, \quad z=54+52t, \quad w=t.$$
