Answer
(a)
$x=1$, $y=-1$.
(b)
$x=2$, $y=4$.
Work Step by Step
(a) The coefficient matrix $A$ is given by
$$A=\left[ \begin {array}{cc} {1}& {2}\\ {1} & {-2} \end {array} \right].$$
One can calculate $A^{-1}$ as follows
$$A^{-1}=\left[ \begin {array}{cc} \frac{1}{2}&\frac{1}{2}\\ \frac{1}{4}&-\frac{1}{4}
\end {array} \right].
$$
The solution is given by
$$\left[ \begin {array}{cc} {x}\\ {y} \end {array} \right]=\left[ \begin {array}{cc} \frac{1}{2}&\frac{1}{2}\\ \frac{1}{4}&-\frac{1}{4}
\end {array} \right]\left[ \begin {array}{cc} {-1}\\ {3} \end {array} \right]=\left[ \begin {array}{c} 1\\ -1\end {array}
\right].
$$
That is, $x=1$, $y=-1$.
(b) The coefficient matrix $A$ is given by
$$A=\left[ \begin {array}{cc} 1&2\\ 1&-2\end {array}
\right]
.$$
One can calculate $A^{-1}$ as follows
$$A^{-1}=\left[ \begin {array}{cc} \frac{1}{2}&\frac{1}{2}\\ \frac{1}{4}&-\frac{1}{4}
\end {array} \right]
.
$$
The solution is given by
$$\left[ \begin {array}{cc} {x}\\ {y} \end {array} \right]=\left[ \begin {array}{cc} \frac{1}{2}&\frac{1}{2}\\ \frac{1}{4}&-\frac{1}{4}
\end {array} \right]\left[ \begin {array}{cc} {10}\\ {-6} \end {array} \right]=\left[ \begin {array}{c} 2\\ 4\end {array}
\right].
$$
That is, $x=2$, $y=4$.
