Question

Show that the following nonlinear systems become linear if we view the unknowns as 1/x,1/y, and 1/z rather than x, y, andz. Use this to find the solution sets of the nonlinear systems. (You must also account for the possibilities that one of x,y,z is zero.) (a) 2x−y +3xy =0 4x+2y−xy =0 (b) yz +3xz−xy =0 yz +2xy =0

Answer 1

let u=1/x, v=1/y , w=1/z
and put those into your equations. what do you get?

Answer 2

I'll try and reply you in other time ... because
now I dont know what I should get .. thanks 4 ur time Phi

Answer 3

for example, the first equation
2x-y+3xy=0
becomes
\[ \frac{2}{u} - \frac{1}{v} +\frac{3}{uv}=0\]
multiply both sides by uv to get
\[ 2v - u + 3 =0 \]
which is linear. Do the same for the other equations

Answer 4

I got it ..I am so glad to talk to you..