First, let's simplify the first equation:
1/x + 1/y = 1/2(2y + 2x)/(xy) = 1/22y + 2x = xy/24y + 4x = xy4y = xy - 4x4y = x(y - 4)
Now we can substitute the expression for 4y into the second equation:
3x - y = 33x - (x(y - 4)) = 33x - xy + 4x = 37x - xy = 3
From here, we can substitute this equation back into the simplified form of the first equation and solve for x and y.
First, let's simplify the first equation:
1/x + 1/y = 1/2
(2y + 2x)/(xy) = 1/2
2y + 2x = xy/2
4y + 4x = xy
4y = xy - 4x
4y = x(y - 4)
Now we can substitute the expression for 4y into the second equation:
3x - y = 3
3x - (x(y - 4)) = 3
3x - xy + 4x = 3
7x - xy = 3
From here, we can substitute this equation back into the simplified form of the first equation and solve for x and y.