Answer
$(x,y) =(3,2)$
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
5x& -&y&=&13\\
2x& +&3y & =&12
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
5&-1 \\
2& 3
\end{vmatrix}=(5)(3)-(2)(-1)=15+2=17$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
13& -1 \\
12& 3
\end{vmatrix}=(13)(3)-(12)(-1)=39+12=51$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
5& 13 \\
2& 12
\end{vmatrix}=(5)(12)-(13)(2)=60-26=34$
By using Cramer's rule we have.
$x=\dfrac{D_x}{D}=\dfrac{51}{17}=3$
and
$y=\dfrac{D_y}{D}=\dfrac{34}{17}=2$
Hence, the solution set is $(x,y) =(3,2)$.
