Solving an equation with three variable.

Question

I am trying to figure out a method (preferably substitution or elimination, please avoid solving by matrices) for this problem.

4x+9y= 8

8x+6z= -1

6y+6z= -1

When all 3 variables (x,y,z) are contained in each equation, I have no problem eliminating one of the variables. Does anyone know an approach for this problem that does NOT include matrices?

Thank You,

Brian

Answer 1

From the 1st equation, get x in terms of y, and substitute for x in the 2nd equation. That leaves a new 2nd equation in y and z only. Now combine the new 2nd equation with the 3rd equation. Both are in y and z only, which you can solve easily for y and z, then plug the result for y into the 1st equation to get x, or plug the result for z into the 2nd equation to get x.

You can also try Cramer's rule, which gives:

x = -288/-576 = 1/2

y = -384/-576 = 2/3

z = 480/-576 = -5/6

Test these answers.