Answer
$\{(3,4)\}$.
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
5x& -3y&=&3\\
7x& +y & =&25
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
5& -3 \\
7& 1
\end{vmatrix}=(5)(1)-(7)(-3)=5+21=26$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
3& -3 \\
25& 1
\end{vmatrix}=(3)(1)-(25)(-3)=3+75=78$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
5& 3 \\
7& 25
\end{vmatrix}=(5)(25)-(7)(3)=125-21=104$
By using Cramer's rule we have.
$x=\frac{D_x}{D}=\frac{78}{26}=3$
and
$y=\frac{D_y}{D}=\frac{104}{26}=4$
Hence, the solution set is $\{(x,y)\} =\{(3,4)\}$.
