SOLUTION: 7x-8y=24 xy^2=1 How do you solve this non linear system.

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Question 1089931: 7x-8y=24
xy^2=1
How do you solve this non linear system.
Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
7x-8y=24
xy^2=1 --> x = 1/y^2
Sub for x in the 1st eqn.
---
7/y^2 - 8y = 24
7 - 8y^3 = 24y^2
8y^3 + 24y^2 - 7 = 0
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y = 0.5 (by graphical methods)
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Divide by (y - 0.5), then solve the quadratic to find the other 2 roots.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!

7x - 8y = 24
xy^2 = 1
x = 1%2Fy%5E2, use this form for substitution in the 1st equation
7%281%2Fy%5E2%29+-+8y+=+24
7%2Fy%5E2+-+8y+=+24
multiply equation by y^2
7+-+8y%5E3+=+24x%5E2
0+=+8y%5E3+%2B+24y%5E2+-+7
solving a cubic equation is tough chore, instead plot this equation
+graph%28+300%2C+200%2C+-4%2C+4%2C+-50%2C+50%2C+8x%5E3%2B24x%5E2-7%29+
one solution: y = .5
:
Use this to find x in the first original equation
7x - 8(.5) = 24
7x - 4 = 24
7x = 24 + 4
7x = 28
x = 28/7
x = 4
:
x=4, y=.5, check in the 2nd original equation
4%2A.5%5E2+=+1
4 * .25 = 1
:
:
Note that y = -2.9 may also be a solution, but x will not be an integer