Question 106520: 2x-y+2z=8
x+2y+4z=3
x+3y-2z=-1
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1st: 2x-y+2z=8
2nd: x+2y+4z=3
3rd: x+3y-2z=-1
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Switch the 1st and 3rd to get a coefficient of one in the upper left-hand corner
1st: x+3y-2z=-1
2nd: 2x-y+2z=8
3rd: x+2y+4z=3
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Multiply 1st by -2 and add to 2nd
Multiply 1st by -1 and add to 3rd:
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1st: x+3y-2z=-1
2nd: 0x-7y+6z=10
3rd: 0x- y+6z=4
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Multiply 3rd by -7 and add to 2nd:
1st: x+3y- 2z=-1
2nd: 0x+0y-36z=-18
3rd: 0x- y+ 6z=4
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Divide thru 2nd by -36 to get:
1st: x+3y- 2z=-1
2nd: 0x+0y+ z=1/2
3rd: 0x- y+ 6z=4
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Since z = 1/2, substitute in 3rd to solve for "y":
-y+6*(1/2) = 4
y = -1
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Since z=(1/2) and y = -1, substitute in 1st to solve for "x":
x + 3(-1) -2(1/2) = -1
x - 3 -1 = -1
x = 3
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Final answer:
x=3, y=-1, z=1/2
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Cheers,
Stan H.
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