Question

Solve each of the following systems of equations by the method of cross-multiplication :
(x + y)/ xy = 2
(x – y)/ xy = 6

Answer 1

$\\ \boxed{\boxed { x = \frac{-1}{2} }\\}\\ \boxed{\boxed { x = \frac{1}{4} }\\ }$

SOLUTION :-

$\\ \frac{x +y}{xy} = 2\\\\\\ \frac{x-y}{xy} = 6$

$(x + y = 2xy) * 3\\x-y = 6xy\\---------\\3x+3y = 6xy\\x-y= 6xy\\ ---------\\2x+4y=0\\\\x+2y=0\\\\\boxed {x=-2y}$

Substitute this value of x

$x+y=2xy\\-2y+y=2(-2y)y\\-y=-4y^{2}\\1=4y\\\boxed{\boxed{y=\frac{1}{4} }}$

Substitute this value of y to get the real value of x

$x=-2y\\x=-2(\frac{1}{4} )\\\\\boxed{\boxed{x= \frac{-1}{2} }}$