Answer
$(1,-2,5)$
Work Step by Step
Step 1. Based on the Cramer’s Rule, with the given equations, we can define the following determinants:
$\begin{array}( \\|D|= \\ \\ \end{array}
\begin{vmatrix}5 &-3&1\\0&4&-6\\7&10&0 \end{vmatrix},
\begin{array}( \\|D_x|= \\ \\ \end{array}
\begin{vmatrix}6 &-3&1\\22&4&-6\\-13&10&0 \end{vmatrix},
\begin{array}( \\|D_y|= \\ \\ \end{array}
\begin{vmatrix}5 &6&1\\0&22&-6\\7&-13&0 \end{vmatrix},
\begin{array}( \\|D_z|= \\ \\ \end{array}
\begin{vmatrix}5 &-3&6\\0&4&22\\7&10&-13 \end{vmatrix}$
Step 2. Evaluate the above determinants:
$|D|=(5)(0+60)-0+(7)(18-4)=398$ (column1 expansion),
$|D_x|=(1)(220+52)-(-6)(60-39)=398$(column3 expansion),
$|D_y|=(5)(0-78)+(7)(-36-22)=-796$ (column1 expansion),
$|D_z|=(5)(-52-220)+(7)(-66-24)=1990$ (column1 expansion)
Step 3. Find the solutions as:
$x=\frac{|D_x|}{|D|}=1$,
$y=\frac{|D_y|}{|D|}=-2$,
$z=\frac{|D_z|}{|D|}=5$
