Answer
$(0,-1,1)$
Work Step by Step
Step 1. Remove fractions by multiplying 30 for the 1st and 2nd equations, 5 for the 3rd equation.
Step 2. Based on the Cramer’s Rule, we can define the following determinants:
$\begin{array}( \\|D|= \\ \\ \end{array}
\begin{vmatrix}10 &-6&15\\-20&12&45\\5&-4&5 \end{vmatrix},
\begin{array}( \\|D_x|= \\ \\ \end{array}
\begin{vmatrix}21 &-6&15\\33&12&45\\9&-4&5 \end{vmatrix},
\begin{array}( \\|D_y|= \\ \\ \end{array}
\begin{vmatrix}10 &21&15\\-20&33&45\\5&9&5 \end{vmatrix},
\begin{array}( \\|D_z|= \\ \\ \end{array}
\begin{vmatrix}10 &-6&21\\-20&12&33\\5&-4&9 \end{vmatrix}$
Step 3. Evaluate the above determinants: (you can also use row operations to create some zeros first)
$|D|=(10)(60+180)-(-20)(-30+60)+(5)(-270-180)=750$ (column1 expansion),
$|D_x|=(21)(60+180)-(33)(-30+60)+(9)(-270-180)=0$ (column1 expansion),
$|D_y|=(10)(165-405)-(-20)(105-135)+(5)(945-495)=-750$ (column1 expansion),
$|D_z|=(10)(108+132)-(-20)(-54+84)+(5)(-198-252)=750$ (column1 expansion),
Step 4. Find the solutions as:
$x=\frac{|D_x|}{|D|}=0$,
$y=\frac{|D_y|}{|D|}=-1$,
$z=\frac{|D_z|}{|D|}=1$
