Solving Equations Using Matrices

A system of two linear equations can be written as a matrix equation. The system ax + by = e and cx + dy = f can be written as ⎡a  b⎣⎡x⎣ = ⎡e⎣, using the coefficient matrix, the inverse, and the determinant to solve for x and y.
⎡c  d⎣⎡y⎣  ⎡f⎣