Algebra Examples

$[\begin{array}{c} x + 9 & - 2 & - 9 y \\ 8 & - 2 x & - 7 \\ 1 & y - 5 & 6 \end{array}] = [\begin{array}{c} 10 x + 0 & - 2 & - 36 \\ 8 & - 2 & - 7 \\ 1 & - 1 & 6 \end{array}]$

Step 1

Add $10 x$ and $0$ .

$[\begin{array}{c} x + 9 & - 2 & - 9 y \\ 8 & - 2 x & - 7 \\ 1 & y - 5 & 6 \end{array}] = [\begin{array}{c} 10 x & - 2 & - 36 \\ 8 & - 2 & - 7 \\ 1 & - 1 & 6 \end{array}]$

Step 2

Write as a linear system of equations.

$x + 9 = 10 x$

$- 2 = - 2$

$- 9 y = - 36$

$8 = 8$

$- 2 x = - 2$

$- 7 = - 7$

$1 = 1$

$y - 5 = - 1$

$6 = 6$

Step 3

Since $6 = 6$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.