# Given the following system #x^2+y^2-z^2+w^2=2 ; x+2y+z^2-3w^2=1# how do I show that if the couple of solution #(x_0,y_0,z_0,w_0)# satisfy #z_0*w_0 != 0# I can find solution for #z# and #w# depending to #x# and #y# ?

##### 1 Answer

Dec 17, 2015

if

#### Explanation:

For eliminating z,

For eliminating w,

So, we got

And you don't want that

For eliminating

If Delta were < 0, there would be no (x,y) such that