Given:
1. x + 2 = 2y
2. 1/x + 1/y = 1
We'll solve equation 1 for x in terms of y:
x = 2y - 2
Now, we'll substitute x = 2y - 2 into equation 2:
1/(2y - 2) + 1/y = 1
Solving this equation, we find y = 2 or y = 1/2.
For y = 2, x = 2.
For y = 1/2, x = 0.
Therefore, the solutions for x and y simultaneously are:
(x, y) = (2, 2)
(x, y) = (0, 1/2)
