If $\begin{bmatrix} 2x - y & 3 \\ 1 & x + 3y \end{bmatrix} = \begin{bmatrix} 5 & 3 \\ 1 & 13 \end{bmatrix}$, what are $x$ and $y$?

Explanation

1. 01

   Equal matrices have equal corresponding elements: $2x - y = 5$ and $x + 3y = 13$.

2. 02

   From the first, $y = 2x - 5$; then $x + 6x - 15 = 13$, so $x = 4$ and $y = 3$.