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
let u=1/x, v=1/y , w=1/z and put those into your equations. what do you get?
I'll try and reply you in other time ... because now I dont know what I should get .. thanks 4 ur time Phi
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
I got it ..I am so glad to talk to you..
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