Problem 4.
(1 point) Consider the following two systems.
(a)
\[
\left\{\begin{array}{c}
x-y=1 \\
x+7 y=3
\end{array}\right.
\]
(b)
\[
\left\{\begin{array}{l}
x-y=3 \\
x+7 y=1
\end{array}\right.
\]
(i) Find the inverse of the (common) coefficient matrix of the two systems.
\[
A^{-1}=\left[\begin{array}{ll}
\square & \square \\
\square & \square
\end{array}\right]
\]
(ii) Find the solutions to the two systems by using the inverse, i.e. by evaluating \( A^{-1} B \) where \( B \) represents the right hand side (i.e. \( B=\left[\begin{array}{l}1 \\ 3\end{array}\right] \) for system (a) and \( B=\left[\begin{array}{l}3 \\ 1\end{array}\right] \) for system (b)).
Solution to system (a): \( x= \) \( \square \) ,\( y= \) \( \square \)
Solution to system (b): \( x= \) \( \square \) ,\( y= \) \( \square \)