Solve `(7)/(x) + (8)/(y) = 2` and `(2)/(x) + (12)/(y) = 20`.

Explanation

Given equations are `(7)/(x) + (8)/(y) = 2 ….(1)`
and `(2)/(x) + (12)/(y) = 20 ….(2)`
Let `(1)/(x)` = u and `(1)/(y)` = v then equation (1) and (2) can be written as
7u + 8v = 2 ….(3)
and 2u + 12v = 20 ….(4)
Multiplying equation (3) by 2 and (4) by 7, we get
14u + 16v = 4 ....(5)
and 14u = 84v = 140 ....(6)
On subtracting equation (6) from (5), we get
-68v =- 136
implies v = 2
Substituting v = 2 in equation (3), we get
7u + 8 `xx` 2 = 2
implies 7u + 16 = 2
implies 7u = - 14 implies u = - 2
When `u = - (1)/(2)` implies `(1)/(x) = - 2` implies `x = - (1)/(2)`
and when v = 2 implies `(1)/(y) = 2` implies `y = (1)/(2)`
Hence, the solution is `{:(x = -(1)/(2)),(y = (1)/(2)):}}`.