Problem 4 : Linear Equation - ( 2002 )

( This problem is taken from Indonesian Entrance Test Of State University - Year 2002 )

If x and y satisfy the equations system 2/x + 1/y = 1 and 1/x - 2/y = 8 then 1/ (x+y) = ....
a. -3/2 b. 5/6 c. 6/5 d. 5 e. 6


Answer :

We take 1/x = p and 1/y = q then it's problem becomes 2p + q = 1 ...(1) and p - 2q =8...(2).
Eliminating q, we obtain : 4p + 2q = 2 .....2x(1)
p - 2q = 8.....1x(2)
------------- +
5p = 10
p = 2
1/x = 2 -----> x = 1/2

p = 2 -----> 2p + q = 1
2.2 + q = 1
4 + q = 1
q = 1- 4 = -3
1/y = -3
y = -1/3
The value of 1/( x+y) is 1/[ 1/2 + (-1/3) ] = 1/ (3/6 - 2/6 ) = 1/ ( 1/ 6) = 6 Answer : E