What is the only ordered pair of real numbers (x,y) that satisfies 7^x-11y=0 and 11^x-7y=0

Question

If possible please include steps and work instead of just the answer.

Answer 1

7^x - 11y = 0   so y = (1/11)7^x

11^x - 7y = 0   so y = (1/7)11^x

 

Set them equal:

 

(1/11)7^x = (1/7)11^x

7/11 = 11^x/7^x

7/11 = (11/7)^x

 

Which only is true when x = -1 since (11/7)^-1 = 7/11.  Plug x = -1 into either equation to find the y-value.