solve for x and y

Question

2^x+3^y is equal to 59
2^x+3-3^y+2 is equal to 13

Answer 1

From the first equation:
2^x + 3^y = 59

From the second equation:
2^x + 3 - 3^y + 2 = 13
2^x - 3^y + 5 = 13

Now, we will use substitution method to solve for x and y.

Let a = 2^x and b = 3^y

Now we have:
a + b = 59 (equation 1)
a - b + 5 = 13 (equation 2)

Adding equation 1 and equation 2:
2a = 72
a = 36

And from equation 1:
36 + b = 59
b = 23

Now, we know:
a = 36 => 2^x = 36 => x = 5
b = 23 => 3^y = 23 => y = 2

Therefore x = 5 and y = 2.