SOLUTION: -5x - 4y + 12z = -140 9x - 8y + z = -649 3x - 2y + 6z = -290 I need to solve this using any method. Id like to see the steps and the correct answer. I think mabye i should

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: -5x - 4y + 12z = -140 9x - 8y + z = -649 3x - 2y + 6z = -290 I need to solve this using any method. Id like to see the steps and the correct answer. I think mabye i should       Log On

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Question 160518: -5x - 4y + 12z = -140
9x - 8y + z = -649
3x - 2y + 6z = -290

I need to solve this using any method. Id like to see the steps and the correct answer. I think mabye i should start by multiplying the 3rd equation by 3 and then subtract it from the 2nd equation? I'm trying to make sence of this but i just cant figure it out. I really appericiate your time, thank you.
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
1.-5x+-+4y+%2B+12z+=+-140
2.9x+-+8y+%2B+z+=+-649
3.3x+-+2y+%2B+6z+=+-290+
How about instead we get rid of y first.
The z coefficients (-4,-8,-2) might be eaiser to start with.
Multiply eq. 1 by -2 and eq. 3 by -4 and add to eq. 2,
9x-8y%2Bz%2B%2810x%2B8y-24z%29=-649%2B280
4.19x-23z=-369
9x-8y%2Bz%2B%28-12x%2B8y-24z%29=-649%2B1160
5.-3x-23z=511
.
.
.
Multiply eq. 5 by (-1) and add to eq. 4 to get rid of z.
19x-23z%2B%283x%2B23z%29=-369-511
22x=-880
highlight%28x=-40%29
From eq. 4,
4.19x-23z=-369
-760-23z=-369
-23z=391
highlight%28z=-17%29
Finally, from eq. 1,
1.-5x+-+4y+%2B+12z+=+-140
200-4y-204=-140
-4y=-136
highlight%28y=34%29