Answer
$$
x=-5 \quad y=7
$$
Work Step by Step
The system can be written as
$$
\underbrace{\left[\begin{array}{ll}
1 & 1 \\
7 & 8
\end{array}\right]}_{\text {Coefficient Matrix }} \cdot\left[\begin{array}{l}
x \\
y
\end{array}\right]=\left[\begin{array}{c}
2 \\
21
\end{array}\right]
$$
Multiply both sides from the left by the inverse of the coefficient matrix. Therefore, the solution is
$$
\left[\begin{array}{l}
x \\
y
\end{array}\right]=\left[\begin{array}{ll}
1 & 1 \\
7 & 8
\end{array}\right]^{-1} \cdot\left[\begin{array}{c}
2 \\
21
\end{array}\right]
$$
The inverse of the matrix
$$
\left[\begin{array}{ll}
a & b \\
c & d
\end{array}\right]
$$
is
$$
\left[\begin{array}{ll}
a & b \\
c & d
\end{array}\right]^{-1}=\frac{1}{a d-b c}\left[\begin{array}{cc}
d & -b \\
-c & a
\end{array}\right]
$$
Here $a=1, b=1, c=7, d=8$, and
$$
\left[\begin{array}{ll}
1 & 1 \\
7 & 8
\end{array}\right]^{-1}=\frac{1}{(1)(8)-(1)(7)}\left[\begin{array}{cc}
8 & -1 \\
-7 & 1
\end{array}\right]=\frac{1}{8-7}\left[\begin{array}{cc}
8 & -1 \\
-7 & 1
\end{array}\right]=\left[\begin{array}{cc}
8 & -1 \\
-7 & 1
\end{array}\right]
$$
So,
$$
\left[\begin{array}{l}
x \\
y
\end{array}\right]=\left[\begin{array}{cc}
8 & -1 \\
-7 & 1
\end{array}\right] \cdot\left[\begin{array}{c}
2 \\
21
\end{array}\right]=\left[\begin{array}{l}
(8)(2)+(-1)(21) \\
(-7)(2)+(1)(21)
\end{array}\right]=\left[\begin{array}{c}
16-21 \\
-14+21
\end{array}\right]=\left[\begin{array}{c}
-5 \\
7
\end{array}\right]
$$
To write it clearly,
$$
\left[\begin{array}{l}
x \\
y
\end{array}\right]=\left[\begin{array}{c}
-5 \\
7
\end{array}\right]
$$
This yields:
$$
x=-5 \quad y=7
$$
