x + y = 5

x^y + y^x = 17
Find x and y

by inspection ... 2 and 3 work

not sure about a "formal" solution method

it's all whole numbers, so there are limited solution possibilities

Thanks Scott. By inspection, the ans is quite obvious I think....something like this..

If x is 2 and y is 3, then 17 could be written as 8 + 9

2^3 + 3^2...I think is not a right approach though.

To find the values of x and y that satisfy the given equations, we can use the method of substitution. Let's solve the first equation for one of the variables and substitute it into the second equation.

From the first equation:
x + y = 5

Solving for y:
y = 5 - x

Substituting this into the second equation:
x^y + y^x = 17 becomes:
x^(5 - x) + (5 - x)^x = 17

Now, we need to consider different values of x and solve for y. We can start by substituting some values of x and checking if the equation is satisfied.

Let's substitute x = 1:
(1)^(5-1) + (5-1)^1 = 1^4 + 4^1 = 1 + 4 = 5 (not equal to 17)

Let's substitute x = 2:
(2)^(5-2) + (5-2)^2 = 2^3 + 3^2 = 8 + 9 = 17

Great! We found a solution where x = 2. Now we can substitute this value into the first equation to solve for y:

x + y = 5
2 + y = 5
y = 5 - 2
y = 3

So, the values of x and y that satisfy both equations are x = 2 and y = 3.