2^x+3^2y=11

2^x+1-3^y=1

x = 1, y = 1

Step-by-step explanation:

Let A = 2^x

Let B = 3^y

A + B² = 11

A = 11 - B²

2A - B = 1

22 - 2B² - B = 1

2B² + B - 21 = 0

2B² + 7B - 6B - 21 = 0

B (2B + 7) - 3 (2B + 7) = 0

(2B + 7) (B - 3) = 0

B = - 7/2, B = 3

A = 11 - 3²

A = 2

2 = 2^x

x = 1

3^y = 3

y = 1