It appears you have the system with augmented matrxi ...
[tex] \left[\begin{array}{cccc|c}4&-5&4&4&3\\-1&1&2&3&1\\3&-4&6&7&4\\-3&3&6&9&3\end{array}\right][/tex]
Right away, you notice that the 4th row is 3 times the 2nd row, so the equations are dependent and will not have a unique solution.
My calculator tells me the reduced equations can be written
... x1 -14x3 -19x4 = -8
... x2 -12x3 -16x4 = -7
This says there are two dependent equations in the set, not just one.
