Expert: Bobby Soltani - 8/16/2004

Question
x-3y+z=-10
3x+2y-z=-11
2x-4y-2z=-46

Answer
Hi Manuel,

There is an easy way to solve three equations with three unknowns using matrices.  But, I will assume that you are not using matrices since you haven't specified so.  Another way is to substitute variables until you solve one, then back substitute until you have all three variables.  Here are sample steps.

1. Solve the first equation for z.  That is, make it look like z = something.
2.  Now plug this value for z into the second and third equations.  The second and third equations will now only have x and y.
3.  Now, the second and third equation represent two equations and two unknowns.  Solve the second one for x.  Make it look like x = something.
4.  Plug this in for x in the third equation.  Now, your third equation will only contain y so you can solve for it.  Then plug your y into the "x = " equation to solve for x.  Then do the same thing above to get z.

I found a good website that explains those steps with an example here --> http://www.allaboutcircuits.com/vol_5/chpt_4/14.html

Scroll down to where they solve three equations and three unknowns.  Please let me know if you still have questions.

Bobby