Question 1058114
.
<pre>
The system of two equations 

{{{x^x}}} + {{{y^y}}} = 31,
x + y = 5

Has two solutions:

     1)  x = 2,  y = 3

and/or

     2)  x = 3,  y = 2.

I don't know if it has other solutions.
</pre>

{{{graph( 330, 330, -2.5, 10.5, -2.5, 50.5,
          x^x + (5-x)^(5-x), 31
)}}}


Plots y = {{{x^x + (5-x)^(5-x)}}}, y = 31


Looking in the plot above, it seems that there are no other solutions.