# Math Help - Matrix Help

1. ## Matrix Help

I need some help solving these two problems. Thank you.

1. 5x-3y=14
-x+2y=10

2. 2x+y=21
3x-2y-2z=4
-x-y-z=5

2. For the first one you can use the matrices:

$\begin{bmatrix} 5 & -3\\ -1 & 2 \end{bmatrix}$ $\begin{bmatrix} x \\ y \end{bmatrix}=$ $\begin{bmatrix}
14 \\ 10\end{bmatrix}$

Then multiply both sides of the equation by the inverse of the 2x2 matrix:

$\begin{bmatrix} x \\ y \end{bmatrix}=$ $\begin{bmatrix}\frac{2}{7} & \frac{3}{7}\\ \frac{1}{7}&\frac{5}{7}\end{bmatrix}$ $\begin{bmatrix}
14 \\ 10\end{bmatrix}$

$\begin{bmatrix} x \\ y \end{bmatrix}=$ $\begin{bmatrix}\frac{58}{7} \\ \frac{64}{7} \end{bmatrix}$

The same process can be used for the second question