Solve by the matrix method: $4x - 3y = -4$ and $2x + 5y = 11$. What is $y$?

Explanation

1. 01

   Write it as $AX = B$ with $A = \begin{bmatrix}4 & -3 \\ 2 & 5\end{bmatrix}$ and $B = \begin{bmatrix}-4 \\ 11\end{bmatrix}$; $|A| = 26$, so $X = A^{-1}B$.

2. 02

   $A^{-1} = \frac{1}{26}\begin{bmatrix}5 & 3 \\ -2 & 4\end{bmatrix}$, and $A^{-1}B = \begin{bmatrix}\frac{1}{2} \\ 2\end{bmatrix}$.

3. 03

   So $x = \frac{1}{2}$ and $y = 2$.