Question

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

Answer 1

One method would be to use Cramer's Rule to get
`color(green)((x,y,z)=(0.970,0.373,0.597))` (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
`color(white)("XXX")`divided by
the determinant of coefficient matrix
`color(white)("XXX")=` the value of the term

Here's what it looks like: