Answer:
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.
