equations
posted by help pls .
solve for x and y
x+y=5
and x^x + y^y = 31
i have found x,y = 2,3 or 3,2
but i got the answer by merely substituting the values...
is there any proper way to find x and y??

this equation is not easily to solve algebraically.
x^x + (5x)^(5x) = 31
can't take logs, or roots, or anything easy. Not sure what doing this kind of exercise is intended to teach.