What is the answer to this simultaneous equation X^x+Y^y=31 and X+Y=5 ?

Question

What is the answer to this simultaneous equation X^x+Y^y=31 and X+Y=5 ?

Answer 1

X^x + Y^y = 31
X + Y = 5
y = 5 - x
x^x + (5 - x)^(5 - x) = 31
x^x + (5 - x)^5/(5 - x)^x = 31
x = 2
y = 3

4 + 27 = 31

Answer 2

x = 5 - y
(5-y) ^ (5-y) + y ^ y = 31 ->>>>>> y = 3 x=2 || x=3 y = 2

Answer 3

x=2, y=3

Answer 4

First step which will probable help is to reinforce and simplify. it particularly is chop up the brackets and then positioned across the words at the same time. (x-3)y + 7 = (x-a million)y - 5 xy - 3y + 7 = xy - y - 5 pass each and each term with a y in it to the left. pass all diverse words to the appropriate. be certain you turn indicators as you turn factors. xy - 3y - xy + y = -5 - 7 positioned across at the same time like words. The useful xy and the unfavourable xy cancel. -2y = -12 Divide the two area by potential of -2. y = 6

Answer 5

Tough to solve other than by trial and error, and one answer has already been found.

If you're trying to check whether that's the ONLY solution, then write it as a function of a single variable, take the derivative, and see if you can make inferences about what the sign of the derivative is.