Need help with solving this system of equations.

x^2 + y^2= 0.5xyz
y^2 + z^2= 0.5xyz
x^2 + z^2= 0.5xyz

I can solve with three variables but I have never ran into a question where the equation was equal to a product of each of the variable so I do not know where to start. If I have a starting point I am pretty sure I can comlete the question on my own.

Subract the 2nd equation from the first, and you see that x = z. Subtract the 3rd from the first and see that y = z. Hence x = y= z. That simplifies things greatly - can you take it from here?

Subract the 2nd equation from the first, and you see that x = z. Subtract the 3rd from the first and see that y = z. Hence x = y= z. That simplifies things greatly - can you take it from here?

I am unsure of what you mean by subtract the second equation from the first. DO you mean like this:

x^2+y^2=0.5xyz
- y^2+z^2=0.5xyz
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I think you have it, but to be clear::

x^2 + y^2 = .5xyz
-(y^2 + z^2 = .5xyz)
--------------------------
x^2 - z^2 = 0

From this you can see that x = z.