Answer
The system can be solved by using Cramer's Rule:
$x_1=1/2$ and $x_2=1/3$
Work Step by Step
The coefficient matrix is $A=\left[\begin{array}{cc}
18&12\\
30&24
\end{array}\right]$
and $|A|=18*24-360=72\ne 0$. Then $A$ is anonsingular matrix
Thus the linear system can be solved by using Cramer's Rule.
Therefore the system has the unique solution:
$x_1=|A_1|/|A|$ and $x_2=|A_2|/|A|$
where, $A_1=\left[\begin{array}{cc}
13&12\\
23&24
\end{array}\right]$
$A_2=\left[\begin{array}{cc}
18&13\\
30&23
\end{array}\right]$
$|A_1=13*24-12*23=36$
$|A_2|=18*23-30*13=24$
$x_1=|A_1|/|A|=36/72=1/2$
and
$x_2=|A_2|/|A|=24/72=1/3$
