2-y+3z=-9,x+3y-z=10,3x+y-z=8

Question

Ordered triple of these equations

Answer 1

We can use one of the equations to find z in terms of the other variables:

z=3x+y-8. Now substitute for z in the other two equations:

2-y+3(3x+y-8)=-9 and x+3y-(3x+y-8)=10.

This reduce to:

2-y+9x+3y-24=-9; 9x+2y=13

and

x+3y-3x-y+8=10; -2x+2y=2 or -x+y=1, and y=x+1.

Substitute for y: 9x+2(x+1)=13, 11x+2=13, 11x=11, so x=1, y=x+1=2 and z=3+2-8=-3.

These values (x,y,z)=(1,2,-3) satisfy all the equations.