For $A = \begin{bmatrix} 2 & 1 \\ -1 & 2 \end{bmatrix}$, $A^{-1} = \frac{1}{5}\begin{bmatrix} 2 & -1 \\ 1 & 2 \end{bmatrix}$. Use it to solve $2x + y = 5$, $-x + 2y = 5$. What is $y$?

Explanation

1. 01

   $X = A^{-1}B = \frac{1}{5}\begin{bmatrix} 2 & -1 \\ 1 & 2 \end{bmatrix}\begin{bmatrix} 5 \\ 5 \end{bmatrix} = \frac{1}{5}\begin{bmatrix} 5 \\ 15 \end{bmatrix}$.

2. 02

   So $x = 1$ and $y = 3$.