Question 249137: My son is having an impossible time with this question; we hope you can help.
He has 3 line equations with 3 variables.
5/x +3y + 62=1
1/x +3(z-y)=9 1/5
2/x +3/5z+y=-1
He has tried the Gaussian(sp) elimination method but cannot quite figure it out.
Can you show him how to do this?
Answer by kensson(21)   (Show Source):
You can put this solution on YOUR website! You can't use Gaussian elimination on a non-linear system. You have to do it with algebra.
(1) 5/x + 3y + 62 = 1
(2) 1/x + 3(z-y) = 46/5
(3) 2/x + 3z/5 + y = -1
Multiply it all through by 5x:
(1) 25 + 15xy = -305x
(2) 5 + 15xz - 15xy = 46x
(3) 10 + 3xz + 5xy = -5x
3*(3) 30 + 9xz + 15xy = -15x
Add (1) and (2) -> (4)
(4) 30 + 15xz = -259x
or: x(15z + 259) = -30
Add (2) and 3*(3) -> (5)
(5) 35 + 24xz = 31x
or: x(24z - 31) = -35
Isolate x and juggle to get:
-30(24z-31) = -35(15z + 259)
-720z + 930 = -525z - 9065
9995 = 195z
This gives z = 199/39*. You can sub that back into (4) or (5) to get x, and both into (1), (2) or (3) to get y.
* I don't believe this is the correct answer to the problem set, but the method is right.
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EDIT
If the first line is 5/x +3y + 6z=1, it comes out more nicely.
5/x +3y + 6z=1
1/x +3(z-y)=9 1/5
2/x +3/5z+y=-1
Let w = 1/z
(1) 5w + 3y + 6z = 1
(2) w - 3y + 3z = 9.2
(3) 2w + y + 0.6z = -1
(1) 5w + 3y + 6z = 1
(4) = 5*(2) 5w - 15y + 15z = 46
(5) = 5*(3) 10w + 5y + 3z = -5
(6) = (1)-(4) 18y - 9z = -45
(7) = 2*(1)-(5) y + 9z = 7
(6)+(7) 19y = -38
So y = -2
From (7) -2 + 9z = 7 so z = 1
From (2) w + 6 +3 = 9.2 so w = 0.2 and x = 5.
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