Solving four non-linear equations

Question

I would like to ask you about solving these four nonlinear equations (x,y,z,w):

axy=x+y

bzw=z+w

cyz=y+z

dxw=x+w

where:

x=y/(ay−1)=w/(dw−1),

z=y/(cy−1)=w/(bw−1)

Thanks, Mehrdad

Answer 1

axy = x+y

axy-y = x

y(ax-1) = x

y = x/(ax-1)

and

axy-x = y

x(ay-1) = y

x = y/(ay-x)

y =x/(ax-1) and x= y/(ay-1)

just switch x and y and you go from the solution for y to the solution for x

dxw = x+w

dxw-w = x

w(dx-1) = x

w = x/(dx-1)