Answer
$(-\frac{87}{26}, \frac{21}{26},\frac{3}{2})$
Work Step by Step
Step 1. Define the following matrices based on the given system of equations:
$\begin{array} \\D=\\ \end{array}
\begin{bmatrix} 2&-1&5\\ -1&7&0\\5&4&3\end{bmatrix},
\begin{array} \\D_x=\\ \end{array}
\begin{bmatrix} 0&-1&5\\ 9&7&0\\-9&4&3\end{bmatrix},
\begin{array} \\D_y=\\ \end{array}
\begin{bmatrix} 2&0&5\\ -1&9&0\\5&-9&3\end{bmatrix},
\begin{array} \\D_z=\\ \end{array}
\begin{bmatrix} 2&-1&0\\ -1&7&9\\5&4&-9\end{bmatrix}$
Step 2. Calculate the determinants of the above matrices (use column 3 expansions):
$|D|=5(-4-35)+3(14-1)=-156$, $|D_x|=5(36+63)+3(0+9)=522$, $|D_y|=5(9-45)+3(18-0)=-126$, $|D_z|=-9(8+5)-9(14-1)=-234$
Step 3. Use the Cramer's Rule:
$x=\frac{|D_x|}{|D|}=-\frac{87}{26}$, $y=\frac{|D_y|}{|D|}=\frac{21}{26}$, $z=\frac{|D_z|}{|D|}=\frac{3}{2}$
Step 4. Conclusion: the solution to the system is $(-\frac{87}{26}, \frac{21}{26},\frac{3}{2})$
