Advertisements
Advertisements
Question
Solve the following pairs of equations:
`(xy)/(x + y) = (6)/(5)`
`(xy)/(y - x)` = 6
Where x + y ≠ 0 and y - x ≠ 0
Advertisements
Solution
`(xy)/(x + y) = (6)/(5)`
⇒ `(x + y)/(xy) = (5)/(6)`
⇒ `(1)/y + (1)/x = (5)/(6)` ....(i)
`(xy)/(y - x)` = 6
⇒ `(y - x)/(xy)` = 6
⇒ `(1)/x + (1)/y = (1)/(6)` ....(ii)
Adding eqns. (i) and (ii), we get
`(2)/x` = 1
⇒ x = 2
⇒ `(1)/y + (1)/(2) = (5)/(6)`
⇒ `(1)/y = (5)/(6) - (1)/(2)`
= `(5 - 3)/(6)`
= `(2)/(6)`
= `(1)/(3)`
⇒ y = 3
Thus, the solution set is (2, 3).
APPEARS IN
RELATED QUESTIONS
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :
3 - (x - 5) = y + 2
2 (x + y) = 4 - 3y
If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.
Solve :
`[ 7 + x ]/5 - [ 2x - y ]/4 = 3y - 5`
`[5y - 7]/2 + [ 4x - 3 ]/6 = 18 - 5x`
Solve the following simultaneous equations:
65x - 33y = 97
33x - 65y = 1
Solve the following pairs of equations:
`(5)/(x + y) - (2)/(x - y)` = -1
`(15)/(x + y) + (7)/(x - y)` = 10.
Solve the following pairs of equations:
`(2)/(3x + 2y) + (3)/(3x - 2y) = (17)/(5)`
`(5)/(3x + 2y) + (1)/(3x - 2y)` = 2
If 2x + y = 23 and 4x - y = 19 : find the value of x - 3y and 5y - 2x.
Can the following equations hold simultaneously?
7y - 3x = 7
5y - 11x = 87
5x + 4y = 43
If yes, find the value of x and y.
Seven more than a 2-digit number is equal to two less than the number obtained by reversing the digits. The sum of the digits is 5. Find the number.
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.
