SOLUTION: I need help with this problem. I have tried everthing. x+2y-z=-4 3x+y-2z=-9 2x-z=-5

Algebra ->  Equations -> SOLUTION: I need help with this problem. I have tried everthing. x+2y-z=-4 3x+y-2z=-9 2x-z=-5      Log On


   

Question 105788: I need help with this problem. I have tried everthing.
x+2y-z=-4
3x+y-2z=-9
2x-z=-5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.x%2B2y-z=-4
2.3x%2By-2z=-9
3.2x-z=-5
Let's use equation 3 to solve for z in terms of x.
3.2x-z=-5
3.-z=-5-2x
3.highlight%28z=5%2B2x%29
Substitute into equations 1 and 2.
1.x%2B2y-z=-4
1.x%2B2y-%285%2B2x%29=-4
1.x%2B2y-5-2x=-4
1.highlight%28-3x%2B2y=1%29
2.3x%2By-2z=-9
2.3x%2By-2%285%2B2x%29=-9
2.3x%2By-10-4x%29=-9
2.highlight%28-x%2By=1%29
Now use equation 2 to solve for y.
2.-x%2By=1
2.y=1%2Bx
Substitute into equation 1.
1.-3x%2B2y=1
1.-3x%2B2%281%2Bx%29=1
1.-3x%2B2%2B2x%29=1
1.-x=-1
1.x=1
Back substitute into 2.
2.y=1%2Bx
2.y=1%2B1
y=2
Back substitute into 3.
3.z=5%2B2x
3.z=5%2B2%281%29
z=7
Check your answers.
1.x%2B2y-z=-4
1.1%2B2%281%29-7=-4
1.3-7=-4
1.-4=-4
Good answer.
2.3x%2By-2z=-9
2.3%281%29%2B1-2%287%29=-9
2.3%2B1-14=-9
2.-9=-9
Good answer.
3.2x-z=-5
3.2%281%29-7=-5
3. -5=-5
Good answer.
x=1, y=1, z=7