Answer
$\{(-1,-6)\}$.
Work Step by Step
We will solve the system using Cramer's method.
First calculate the determinant D consisting of the x− and y− coefficients.
$D=\begin{vmatrix}
4& -3\\
3 & -1
\end{vmatrix} =(4)(-1)−(3)(-3)=-4+9=5$.
For determinant Dx replace the x− coefficients with the constants.
$D_x=\begin{vmatrix}
14& -3\\
3 & -1
\end{vmatrix} =(14)(−1)−(3)(-3)=-14+9=-5$.
For determinant Dy replace the y− coefficients with the constants.
$D_y=\begin{vmatrix}
4& 14\\
3 & 3
\end{vmatrix} =(4)(3)−(3)(14)=12-42=-30$.
By using Cramer's rule we have.
$x=\frac{D_x}{D}=\frac{-5}{5}=-1$
And
$y=\frac{D_y}{D}=\frac{-30}{5}=-6$
Hence, the solution set is $\{(x,y)\}=\{(-1,-6)\}$.
