Solve the Matrix Equation [[x+2,-2],[y-1,x+1]]=[[8,-2],[2y+5,7]]

$[\begin{array}{c} x + 2 & - 2 \\ y - 1 & x + 1 \end{array}] = [\begin{array}{c} 8 & - 2 \\ 2 y + 5 & 7 \end{array}]$

Step 1

Write as a linear system of equations.

$x + 2 = 8 - 2 = - 2 y - 1 = 2 y + 5 x + 1 = 7$

Step 2

Since $- 2 = - 2$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.