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) (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
----------
y = 0.5 (by graphical methods)
=========
Divide by (y - 0.5), then solve the quadratic to find the other 2 roots.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
7x - 8y = 24
xy^2 = 1
x = , use this form for substitution in the 1st equation
multiply equation by y^2
solving a cubic equation is tough chore, instead plot this equation
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 * .25 = 1
:
:
Note that y = -2.9 may also be a solution, but x will not be an integer
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