# How do you solve 8x-2y+5z=10, -2x+10y-3z=0, and -5x-3y+10z=0 using matrices?

Aug 20, 2016

One method would be to use Cramer's Rule to get
$\textcolor{g r e e n}{\left(x , y , z\right) = \left(0.970 , 0.373 , 0.597\right)}$ (to 3 places for each)

#### Explanation:

Cramer's Rule tells us that the quotient of:
the determinant of the coefficient matrix with the term's column replaced by the answer column
$\textcolor{w h i t e}{\text{XXX}}$divided by
the determinant of coefficient matrix
$\textcolor{w h i t e}{\text{XXX}} =$ the value of the term

Here's what it looks like: