Answer
Solution set = $\{(7,4)\}$
Work Step by Step
Rewrite the system:
$\left\{\begin{array}{l}
2x-3y=2\\
5x+4y=51
\end{array}\right.$
$D= $determinant of the coefficient matrix
$=\left|\begin{array}{ll}
2 & -3\\
5 & 4
\end{array}\right|=2(4)-(-3)(5)=23$
$D_{x}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
2 & -3\\
51 & 4
\end{array}\right|=8+153=161$
$D_{y}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
2 & 2\\
5 & 51
\end{array}\right|=102-10=92$
$x=\displaystyle \frac{D_{x}}{D}=\frac{161}{23}=7$
$y=\displaystyle \frac{D_{y}}{D}=\frac{92}{23}=4$
Solution set = $\{(7,4)\}$
