Math Is Fun Forum

engrymbiff

Member

Registered: 2010-06-14

Posts: 30

Find all real sol. to the following system of eq.

Find all real sol. to the following:

How to do this?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Find all real sol. to the following system of eq.

hi engrymbiff

step 1.  Square the first equation.

step 2.  Use the second equation to eliminate x squared plus y squared and then cancel z squared.

step 3.  Rearrange the third equation to make xy the subject.  Use this in the equation from step 2 and you are left with just 'z's.

step 4.  Rearrange to make a quadratic in z.  It factorises to give two values of z.

step 5. Now use this value to get x and y.  As the equations are 'symmetrical' in x and y, you can have these values either way round.

Bob

Last edited by Bob (2011-12-12 06:59:55)

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