Twice the sum of two numbers exceeds three times their difference by 8, while half the sum is one more than the difference. What are the numbers?

Answer 1

2(x+y) = 3(x-y)+8

2x+2y = 3x-3y + 8

5y = x + 8

(x+y)/2 = 1 + (x-y)

x+y = 2 + 2x-2y

3y = 2+x

5y = 8+x

2y = 6

y = 3

x = 7