Write the system as an augmented matrix:
[tex]\left[\begin{array}{cc|c}1&5&22\\4&-7&7\end{array}\right][/tex]
Add -4 (row 1) to row 2 :
[tex]\left[\begin{array}{cc|c}1&5&22\\0&-27&-81\end{array}\right][/tex]
Multiply row 2 by -1/27 :
[tex]\left[\begin{array}{cc|c}1&5&22\\0&1&3\end{array}\right][/tex]
Add -5 (row 2) to row 1 :
[tex]\left[\begin{array}{cc|c}1&0&7\\0&1&3\end{array}\right][/tex]
Then x = 7 and y = 3.
