Answer
$\{(5,3)\}$.
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
7x& -6y&=&17\\
3x& +y & =&18
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
7& -6 \\
3& 1
\end{vmatrix}=(7)(1)-(3)(-6)=7+18=25$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
17& -6 \\
18& 1
\end{vmatrix}=(17)(1)-(18)(-6)=17+108=125$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
7& 17 \\
3& 18
\end{vmatrix}=(7)(18)-(3)(17)=126-51=75$
By using Cramer's rule we have.
$x=\frac{D_x}{D}=\frac{125}{25}=5$
and
$y=\frac{D_y}{D}=\frac{75}{25}=3$
Hence, the solution set is $\{(x,y)\} =\{(5,3)\}$.
