​ Solve the following systems of equations: x + y = 2xy (x - y)/xy = 6, x ≠ 0, y ≠ 0 ​

Question

Solve the following systems of equations:

x + y = 2xy

\(\frac{x-y}{xy}\) = 6, x ≠ 0, y ≠ 0

Answer 1

x + y = 2xy

x – y = 6xy

Adding the two equation

⇒ 2x = 8xy

⇒ y = 1/4

Thus,

x + 1/4 = 2 × x × 1/4

⇒ x/2 = - 1/4

⇒ x = - 1/2