Answer
$(\frac{189}{29},-\frac{108}{29},\frac{88}{29})$
Work Step by Step
Step 1. Based on the Cramer’s Rule, with the given equations, we can define the following determinants:
$\begin{array}( \\|D|= \\ \\ \end{array}
\begin{vmatrix}0 &3&5\\2&0&-1\\4&7&0 \end{vmatrix},
\begin{array}( \\|D_x|= \\ \\ \end{array}
\begin{vmatrix} 4&3&5\\10&0&-1\\0&7&0\end{vmatrix},
\begin{array}( \\|D_y|= \\ \\ \end{array}
\begin{vmatrix}0 &4&5\\2&10&-1\\4&0&0\end{vmatrix},
\begin{array}( \\|D_z|= \\ \\ \end{array}
\begin{vmatrix}0 &3&4\\2&0&10\\4&7&0\end{vmatrix}$
Step 2. Evaluate the above determinants:
$|D|=(4)(-3-0)-(7)(0-10)=58$ (row3 expansion),
$|D_x|=-(7)(-4-50)=378$ ((row3 expansion),
$|D_y|=(4)(-4-50)=-216$ ((row3 expansion),
$|D_z|=(4)(30-0)-(7)(0-8)=176$ ((row3 expansion),
Step 3. Find the solutions as:
$x=\frac{|D_x|}{|D|}=\frac{189}{29}$,
$y=\frac{|D_y|}{|D|}=-\frac{108}{29}$,
$z=\frac{|D_z|}{|D|}=\frac{88}{29}$
