1/y+4/x= 1
∴x+y=(x+y)*( 1/y+4/x)
=5+x/y+4y/x≥5+2*√(x/y)*(4y/x)
=9
Take "=" if and only if x/y=4y/x, that is, x = 6 and y = 3.
That is, the minimum value of x+y is 9.
Comments: Looking at the substitution and mean inequality of "1", this question is slightly clever, and it needs to be divided by xy to get 1 and then calculated.