System of equations

Question

Can someone help me with solving this system of equations:

ln(y)-y/(2*x)=0

(x/y)-x^(1/2)=0

Answer 1

From second equation: x/y = x^1/2 y/x = x^-1/2 y = sqrt(x) and x = y²

From first equation with x substituted:

ln(y) = y/(2y²)

ylny = 1/2 which has the solution:

y = e^W(1/2) where W is called the product log function.

y = 1.42153 from Wolfram Alpha

Please consider a tutor. Take care.