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Βασίλης Κέκεσης
May 18, 2020

pls help me with this system of equations

yz-λy-λz=0

xz-λx-λz=0

xy-λx-λy=0

xy+xz+yz=150

I have to solve for x,y,z,λ

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Ian Fowler
May 18, 2020  ·  Edited: May 18, 2020

First, note that L(ambda) <> 0 since that would the 4th equation impossible.


I'll get you started and see if you can finish. Re-arrange each equation:

1) yz = L(y+z)

2) xz = L(x+z)

3) xy = L(x+y)

Now take (1) divided by (2) and see if you can get a relationship between x and y. If you can, that will tell you how to get a relationship between x and z. The rest will tumble down. Let me know how you make out.





Βασίλης Κέκεσης
May 19, 2020

Well first I forgot to tell you that in my initial problem x,y,z>0

Anyway what you said actually worked thank you very much

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