Solve 3 equations algebraically

Question

Solve algebraically. 6x-3y+8z=4 -x+9y-2z=2 4x+6y-4z=3

Answer 1

Label equations A, B, C:

A: 6x-3y+8z=4

B: -x+9y-2z=2

C: 4x+6y-4z=3

Manipulate the equations and add more labels:

D: A+2C: 14x+9y=10

E: C-2B: 6x-12y=-1

F: 4D+3E: 74x=37, x=37/74=1/2, substitute for x in E: 3-12y=-1, 12y=4, y=1/3.

Substitute for x and y in B: -1/2+3-2z=2; 2z=1/2, z=1/4.

CHECK: substitute for x, y, z in A, B, C:

3-1+2=4; OK!

-1/2+3-1/2=2; OK!

2+2-1=3; OK!

All OK, so solution is x=1/2, y=1/3, z=1/4.