The values of x and y are: y = 1/4 and x = -2
How to solve simultaneous equations?
The simultaneous equations are given as:
xy/(x + y) = 1/2 ----(1)
xy/(x - y) = 1/6 ----(2)
Cross multiply in the first equation to get:
2xy = x + y
2xy - x = y
x(2y - 1) = y
x = y/(2y - 1)
Cross multiply in the 2ns equation to get:
6xy = x - y ----(3)
Put y/(2y - 1) for x in eq 3 to get:
6(y/(2y - 1))y = (y/(2y - 1)) - y
Multiply through by y/(2y - 1) to get:
6y² = y - 2y² + y
8y² = 2y
y = 1/4
x = 4/(2(1/4) - 1)
x = -2