Question

if x and y satisfy the equations xy=1 and
1/y - 3/x = 1/2
then the value of x+y=

Answer 1

Start
xy = 1
1/y - 3/x = 1/2

For the latter equation, let us clear the fractions by multiplying by 2xy
this gives - 2x - 6y = xy
Now let us substitute y = 1/x from the first given equation into this one.
2x - 6*(1/x) = x * (1/x)

2x - 6/x = 1. Multiply through by x.
2x^2 - x - 6 = 0. After bringing the x to the LHS.

We can factor this (or use quadratic formula).
(2x + 3)(x - 2) = 0 works.
Therefore x = 2, and x = -3/2. are solutions
Plugging this into y = 1/x gives us two solution coordinates
(2,1/2) and (-3/2, -2/3) namely.
For the first pair x+y is 5/2.
For the second pair x+y is -13/6.

Answer 2

The option are given are

A. -7/8 OR 5/6
B. -2/3 OR -3/4
C.-1/1/4 OR 1/2/3
D. -3/1/3 OR 1/1/2
E. -2/1/6 OR 2/1/2
@Miracrown

Answer 3

Yes, okay, so we have the right answers
I am just trying to match that with the representation in the answers you gave

E presents them as mixed fractions
Know what I mean? @HemarubenY

Answer 4

sorry ! i didn't notice that .. thank you for ur guide ! @Miracrown

Answer 5

no worries, but do you understand it all?
Any doubts? - don't hesitate to share it with me... ;)

Answer 6

No doubts .. thanks :) @Miracrown