Answer
Since $\det(A)\neq 0$, then the system has a unique solution.
Work Step by Step
Let $A$ be the coefficient matrix which is given by
$$A=\left[ \begin {array}{ccc} -1&1&2\\ 2&3&1
\\ 5&4&2\end {array} \right]=\left[ \begin {array}{ccc} -1&1&2\\ 0&5&5
\\ 0&9&12\end {array} \right]
.$$
One can calculate $\det(A)$ as follows
$$\det(A)=-(5)(12)+(5)(9)=-60+45=-51.$$
Since $\det(A)\neq 0$, then the system has a unique solution.