Answer
The system can be solved by using Cramer's Rule:
$x_1=2$ and $x_2=-2$
Work Step by Step
The coefficient matrix is
$A=\left[\begin {array}{cc}
3&4\\
5&3
\end{array}\right]$
and $|A|=-11 \neq0 $. Then $ A$ is a nonsingular matrix such that
$AX=B$, where $X=\left[\begin {array}{c}
x_1\\
x_2
\end{array}\right]$ and
$B=\left[\begin {array}{c}
-2\\
4
\end{array}\right]$
since $A$ is a nonsingular matrix, then we can use Cramer's Rule to solve the linear system. Thus the linear system has the unique solution
$x_1=|A_1|/|A|$ and $x_2=|A_2|/|A|$
where $A_1=\left[\begin {array}{c}
-2&4\\
4&3
\end{array}\right]$
$A_2=\left[\begin {array}{c}
3&-2\\
5&4
\end{array}\right]$
and then $|A_1|=-22 $ and $|A_2|=22$
therefore, $x_1=|A_1|/|A|=22/11=2$ and $x_2=|A_2|/|A|=-22/11=-2$
