To solve this system of equations, we can use substitution or elimination method. Let's use substitution method.

From the first equation, we can rearrange it to solve for x:
x = y + 7

Substituting this value of x into the second equation:
1/(y + 7) + 1/y = 1/12

To simplify the equation, we can find a common denominator:
(y + 7 + y) / (y(y + 7)) = 1/12

Combining like terms:
(2y + 7) / (y^2 + 7y) = 1/12

Cross multiplying:
12(2y + 7) = y^2 + 7y

Expanding:
24y + 84 = y^2 + 7y

Rearranging the equation:
y^2 - 17y - 84 = 0

Factoring the quadratic equation:
(y - 21)(y + 4) = 0

Setting each factor equal to zero:
y - 21 = 0 or y + 4 = 0

Solving for y:
y = 21 or y = -4

Substituting these values back into the first equation to solve for x:
For y = 21:
x - 21 = 7
x = 28

For y = -4:
x - (-4) = 7
x + 4 = 7
x = 3

Therefore, the solutions to the system of equations are (x, y) = (28, 21) and (3, -4).