Answer
$\{(\frac{20}{11},-\frac{14}{11})\}$.
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
3x& -2y&=&8\\
2x& -5y & =&10
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
3& -2 \\
2& -5
\end{vmatrix}=(3)(-5)-(2)(-2)=-15+4=-11$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
8& -2 \\
10& -5
\end{vmatrix}=(8)(-5)-(10)(-2)=-40+20=-20$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
3& 8 \\
2& 10
\end{vmatrix}=(3)(10)-(2)(8)=30-16=14$
By using Cramer's rule we have.
$x=\frac{D_x}{D}=\frac{-20}{-11}=\frac{20}{11}$
and
$y=\frac{D_y}{D}=\frac{14}{-11}=-\frac{14}{11}$
Hence, the solution set is $\{(x,y)\} =\{(\frac{20}{11},-\frac{14}{11})\}$.
