Answer
$(\frac{22}{5},\frac{24}{25},\frac{66}{25})$
Work Step by Step
Step 1. Based on the Cramer’s Rule, with the given equations, we can define the following determinants:
$\begin{array}( \\|D|= \\ \\ \end{array}
\begin{vmatrix}2 &-5&0\\1&1&-1\\3&0&5 \end{vmatrix},
\begin{array}( \\|D_x|= \\ \\ \end{array}
\begin{vmatrix}4 &-5&0\\8&1&-1\\0&0&5 \end{vmatrix},
\begin{array}( \\|D_y|= \\ \\ \end{array}
\begin{vmatrix}2 &4&0\\1&8&-1\\3&0&5 \end{vmatrix},
\begin{array}( \\|D_z|= \\ \\ \end{array}
\begin{vmatrix}2 &-5&4\\1&1&8\\3&0&0
\end{vmatrix}$
Step 2. Evaluate the above determinants:
$|D|=(3)(5-0)+(5)(2+5)=50$ (row3 expansion),
$|D_x|=(5)(4+40)=220$ (row3 expansion),
$|D_y|=(3)(-4-0)+(5)(16-4)=48$ (row3 expansion),
$|D_z|=(3)(-40-4)=132$ (row3 expansion),
Step 3. Find the solutions as:
$x=\frac{|D_x|}{|D|}=\frac{22}{5}$,
$y=\frac{|D_y|}{|D|}=\frac{24}{25}$,
$z=\frac{|D_z|}{|D|}=\frac{66}{25}$
