I presume the second equation is actually:

2^{x - 1} + 3^{y + 1} = 35

Please use parenthesis!!

We know that 3^y = 2^x - 7

So...

2^{x - 1} + 3^{y + 1} = 35

(1/2)*2^x + 3*3^y = 35

(1/2)*2^x + 3*[2^x - 7] = 35

(1/2)*2^x + 3*2^x - 21 = 35

(7/2)*2^x = 56

2^x = (2/7)*56 = 16

2^x = 2^4

Thus x = 4 and 3^y = 2^4 - 7 = 16 - 7 = 9

So y = 2

-Dan