Find the ordered triple of these equations

x-2y+2z=-2

2x+3y-z=0

3x+2y+3z=-15
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1 Answer

Call the equations in order A, B and C.

A+C: D: 4x+5z=-17;

2B-3C: 4x+6y-2z-(9x+6y+9z)=0-(-45); -5x-11z=45 or E: 5x+11z=-45.

4E-5D: 44z-25z=-180+85; 19z=-95, z=-5. Therefore 4x=-17+25=8, so x=2.

Use any equation to find y by substituting for x and z:  2y=x+2z+2=2-10+2=-6, so y=-3.

Now check out these values in all original equations:

2+6-10=-2; 4-9+5=0; 6-6-15=-15. All check out so the solution is (2,-3,-5) for (x,y,z).
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