Algebra -> Test -> SOLUTION: If 1/x+1/y=1/4 and 1/x-1/y=3/4,then x= (A)1/4 (B)1/2 (C)1 (D)2 (E)4 Thank you so much! Log On

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Question 473678: If 1/x+1/y=1/4 and 1/x-1/y=3/4,then x=
(A)1/4
(B)1/2
(C)1
(D)2
(E)4
Thank you so much!
Found 2 solutions by Theo, MathTherapy:Answer by Theo(10232) (Show Source):
You can put this solution on YOUR website!
the equations you have to work with are:
1/x + 1/y = 1/4 (first equation)
1/x - 1/y = 3/4 (second equation)
solve these 2 equations simultaneously to get your answer.
use the first equation to solve for 1/x.
1/x + 1/y = 1/4 becomes 1/x = 1/4 - 1/y
we can substitute for 1/x in the second equation to get:
1/x - 1/y = 3/4 becomes:
(1/4 - 1/y) - 1/y = 3/4
simplify this to get:
1/4 - 1/y - 1/y = 3/4
combine like terms to get:
1/4 - 2/y = 3/4
subtract 1/4 from both sides of this equation to get:
-2/y = 1/2
divide both sides of this equation by -2 to ge4t:
1/y = -1/4
now that we know what 1/y is equal to, we can solve for 1/x.
use the first equation of:
1/x + 1/y = 1/4
substitute -1/4 for 1/y to get:
1/x - 1/4 = 1/4
add 1/4 to both sides of this equation to get:
1/x = 1/2
you now have:
1/x = 1/2
1/y = -1/4
solve for x in the first of these 2 equations.
1/x = 1/2 is the equation.
multiply both sides of this equation by x to get:
1 = x/2
multiply both sides of this equation by 2 to get:
2 = x which is the same as x = 2.
that's your answer.
selection D contains it.
similarly, we can solve for y to get y = -4
we have x = 2 and y = -4
substitute in your original equations to see that these solutions are good for both equations.
1/x + 1/y = 1/4 becomes 1/2 - 1/4 = 1/4 which is true.
1/x - 1/y = 3/4 becomes 1/2 + 1/4 = 3/4 which is also true.

Answer by MathTherapy(8819) (Show Source):
You can put this solution on YOUR website!
Move it to a better place:
If 1/x+1/y=1/4 and 1/x-1/y=3/4,then x=
(A)1/4
(B)1/2
(C)1
(D)2
(E)4
Thank you so much!
------ eq (i) becomes:
4y + 4x = xy -------- Multiplying equation by LCD, 4xy
------ eq (ii) becomes:
4y - 4x = 3xy -------- Multiplying equation by LCD, 4xy
4y + 4x = xy -------- eq (i)
4y - 4x = 3xy -------- eq (ii)
8y = 4xy -------- Adding eq (i) & (ii)
--------> x = (CHOICE D)

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