If 3^x + 2^y = 985 and 3^x - 2^y = 473, find the value of x + y.

x = 6 and y = 8

Step-by-step explanation:

3^x + 2^y = 985 and 3^x - 2^y = 473 can be written in column form:

3^x + 2^y = 985

3^x - 2^y = 473

By summing these two equations we temporarily eliminate y:

2*3^x = 985 + 473 = 1458

Then 2*3^x = 1458. We must find x.

Dividing both sides by 2 yields

3^x = 729

Note that 729 = 3^6. Therefore, x must be 6.

If x = 6, then the first equation becomes

3^6 + 2^y = 985, or

729 + 2^y = 985, or 2^y = 985 - 729 = 256

Note that 2^y = 256 = 2^8. Then y must be 8.