Equations

[vinay1983]

3/(x+y) + 2/(x-y) = 3/2

9/(x+y) - 4/(x-y)= -1/2


Solve the equations.

[ganeshrkamath]

3/(x+y) + 2/(x-y) = 3/2

9/(x+y) - 4/(x-y)= -1/2


Solve the equations.

Let A = 1/(x+y) and B = 1/(x-y)

We get
3A + 2B = 3/2 or 6A + 4B = 3______________________(1)
and
9A - 4B = -1/2______________________(2)

(1) + (2) :
15A = 5/2
A = 1/6
Substitute this in (1)
1 + 4B = 3
4B = 2
B = 1/2

So 1/(x+y) = 1/6 and 1/(x-y) = 1/2
So (x+y) = 6 and (x-y) = 2
[spoiler]x = 4, y = 2[/spoiler]

Cheers

[GMATGuruNY]

3/(x+y) + 2/(x-y) = 3/2

9/(x+y) - 4/(x-y)= -1/2


Solve the equations.

To clear the coefficients in red, multiply the first equation by 2:
6/(x+y) + 4/(x-y) = 6/2.

Add the equations and simplify:
6/(x+y) + 4/(x-y) = 6/2.
9/(x+y) - 4/(x-y) = -1/2
_________________________
15/(x+y) = 5/2
30 = 5(x+y)
x+y = 6.

To clear the coefficients in blue, multiply the first equation by -3:
-9/(x+y) - 6/(x-y) = -9/2.

Add the equations and simplify:
-9/(x+y) - 6/(x-y) = -9/2.
9/(x+y) - 4/(x-y) = -1/2
_________________________
-10/(x-y) =-10/2
-20 = -10(x-y)
x-y = 2.

Add together the resulting equations:
x+y = 6
x-y = 2
________
2x = 8
x = 4.

Substitute x=4 into x+y=6:
4+y=6
y = 2.

Thus, x=4 and y=2.