Question

`x+y=5` and `x^y+y^x=17` Find the value of `x and y`?

Answer 1

`x=2, y=3`
Assuming `{x,y} in NN`

Explanation:

Here we have two equations:

`x+y =5`

`x^y+y^x=17`

{Although there is no resaon to assume that `x` and `y` are naturals, it seemed like a sensible place to start.}

Assume `{x,y} in NN`

Since `x+y = 5`

`x in { 1, 2, 3, 4}` and `y in {4, 3, 2, 1}`

Testing each `(x, y)` pair in turn we notice that:

`2^3+3^2 = 8 + 9 =17`

Hence a solution to this system is `x=2, y=3`

NB: I have not worked through the cases where `(x, y) in RR`, Hence, I have not proved that there are no other real solutions to this system.