Question

2x-y+2z=-7
-x+2y-4z=5
x+4y-6z=-1

Solve The System Using The Elimination Method.

Answer 1

adding eqautions 2 and 3 you elimnate the x and get: 6y-10z=4 (eqn3')
mutlt (eqn2) by 2 and add it to (eqn1) to get: 3y-6z=3 (eqn1')
now solve the system involving (eqn3') and (eqn1') for y and z by mutliplying (eqn1') by -2, and then adding the two equations together

6y-10z=4 eqn3'
-6y+12z=-6 (eqn1'')
2z=-2
z=-1

back sub to get y using (eqn1'):
3y-6(-1)=3
3y=-3
y=-1

now go back to the orginial (eqn3) to get x:

x+4(-1)-6(-1)=-1
x-4+6=-1
x=-3

thus the solution set is the ordered triple {(-3, -1, -1)}

(assuming no arith. errors!)