## Elementary Linear Algebra 7th Edition

Since $\det(A)\neq 0$, then the system has a unique solution.
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.