Answer
$(0.4,-1)$
Work Step by Step
Step 1. Based on the Cramer’s Rule, with the given equations, we can define the following determinants:
$\begin{array}( \\|D|= \\ \\ \end{array}
\begin{vmatrix} 10 &-17\\20 &-31 \end{vmatrix},
\begin{array}( \\|D_x|= \\ \\ \end{array}
\begin{vmatrix} 21 &-17\\39 &-31 \end{vmatrix},
\begin{array}( \\|D_y|= \\ \\ \end{array}
\begin{vmatrix} 10 &21\\20 &39 \end{vmatrix}$
Step 2. Evaluate the above determinants:
$|D|=-10\times31-(-17\times20)=30$,
$|D_x|=-21\times31-(-17\times39)=12$,
$|D_y|=10\times39)-(21\times20)=-30$
Step 3. Find the solutions as:
$x=\frac{|D_x|}{|D|}=\frac{2}{5}=0.4$,
$y=\frac{|D_y|}{|D|}=-1$
