Advertisements
Advertisements
Question
Solve the following pairs of equations:
`(x + y)/(xy)` = 2
`(x - y)/(xy)` = 6
Advertisements
Solution
`(x + y)/(xy)` = 2
⇒ x + y = 2xy ....(i)
`(x - y)/(xy)` = 6
⇒ x - y = 6xy ....(ii)
Adding eqns. (i) and (ii), we get
2x = 8xy
⇒ y = `(1)/(4)`
Substituting the value of y in eqn. (i), we get
`x + (1)/(4) = 2x xx (1)/(4)`
⇒ `(4x + 1)/(4) = x/(2)`
⇒ 8x + 2 = 4x
⇒ 4x = -2
⇒ x = `-(1)/(2)`
Thus, the solution set is `(-1/2, 1/4)`.
APPEARS IN
RELATED QUESTIONS
Find the value of m, if x = 2, y = 1 is a solution of the equation 2x + 3y = m.
Solve the following simultaneous equations :
3(2u + v) = 7uv
3(u + 3v) = 11uv
Solve the following pairs of equations:
`x/(3) + y/(4)` = 11
`(5x)/(6) - y/(3)` = -7
Solve the following pairs of equations:
`(2)/(x + 1) - (1)/(y - 1) = (1)/(2)`
`(1)/(x + 1) + (2)/(y - 1) = (5)/(2)`
Can the following equations hold simultaneously?
7y - 3x = 7
5y - 11x = 87
5x + 4y = 43
If yes, find the value of x and y.
If 2 is added to the numerator and denominator it becomes `(9)/(10)` and if 3 is subtracted from the numerator and denominator it becomes `(4)/(5) `Find the fraction.
The ratio of two numbers is `(2)/(5)`. If 4 is added in first and 32 is subtracted from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.
A boat goes 18 km upstream in 3 hours and 24 km downstream in 2 hours. Find the speed of the boat in still water and the speed of the stream.
Sunil and Kafeel both have some oranges. If Sunil gives 2 oranges to Kafeel, then Kafeel will have thrice as many as Sunil. And if Kafeel gives 2 oranges to Sunil, then they will have the same numbers of oranges. How many oranges does each have?
A and B can build a wall in `6(2)/(3)` days. If A's one day work is `1(1)/(4)` of one day work of B, find in 4 how many days A and B alone can build the wall.
