Answer
$\{(-3,2)\}$.
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
3x& +4y&=&-1\\
-2x& +y & =&8
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
3& 4 \\
-2& 1
\end{vmatrix}=(3)(1)-(-2)(4)=3+8=11$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
-1& 4 \\
8& 1
\end{vmatrix}=(-1)(1)-(8)(4)=-1-32=-33$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
3& -1 \\
-2& 8
\end{vmatrix}=(3)(8)-(-2)(-1)=24-2=22$
By using Cramer's rule we have.
$x=\frac{D_x}{D}=\frac{-33}{11}=-3$
and
$y=\frac{D_y}{D}=\frac{22}{11}=2$
Hence, the solution set is $\{(x,y)\} =\{(-3,2)\}$.
