Solving a 3x3 system of equation

[RicardoPB]

Hello everyone so I was wondering how to solve this 3x3 system

 

[Romsek]

assuming neither [MATH]x[/MATH] nor [MATH]y[/MATH] is zero divide (1) by (2)

It's pretty straightforward if tedious from there. Be very careful keeping track of signs.

 

[Steven G]

If y=0, then it follows that x=0. By symmetry if x=0, then y=0. But if this was the case then x^2 + y^2 = 8 could not be, so it is not the case that x=y=0. So you can divide without any concerns.