Answer
$(x,y) =(-1,2)$
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
x& +&3y&=&5\\
2x& -&3y & =&-8
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
1&3 \\
2& -3
\end{vmatrix}=(1)(-3)-(2)(3)=-3-6=-9$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
5&3 \\
-8& -3
\end{vmatrix}=(5)(-3)-(-8)(3)=-15+24=9$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
1&5 \\
2& -8
\end{vmatrix}=(1)(-8)-(2)(5)=-8-10=-18$
By using Cramer's rule we have.
$x=\dfrac{D_x}{D}=\dfrac{9}{-9}=-1$
and
$y=\dfrac{D_y}{D}=\dfrac{-18}{-9}=2$
Hence, the solution set is $(x,y) =(-1,2)$.
