X^x+y^y=31

x+y=5
plz help i was told to use newton litrate method
plz help

x + y = 5

Possible combinations :

x = 1 , y = 4

x = 2 , y = 3

x = 3 , y = 2

x = 4 , y = 1

x = 1 , y = 4

x ^ x + y ^ y = 31

1 ^ 2 + 2 ^ 2 = 31

1 + 4 = 31

Incorrect.

x = 2 , y = 3

x ^ x + y ^ y = 31

2 ^ 2 + 3 ^ 3 = 31

4 + 27 = 31

Correct.

x = 3 , y = 2

x ^ x + y ^ y = 31

3 ^ 3 + 2 ^ 2 = 31

27 + 4 = 31

Correct.

x = 4 , y = 1

x ^ x + y ^ y = 31

4 ^ 4 + 1 ^ 1 = 31

256 + 1 = 31

Incorrect.

The solutions are :

x = 2 , y = 3

and

x = 3 , y = 2