Advertisements
Advertisements
प्रश्न
Solve for x and y:
`5/x - 3/y = 1, 3/(2x )+ 2/(3y) = 5`
उत्तर
The given equations are:
`5/x - 3/y = 1` ……..(i)
`3/(2x )+ 2/(3y) = 5` ……..(ii)
Putting` 1/x = u and 1/y`= v, we get:
5u - 3v = 1 …….(iii)
⇒`3/2 u + 2/3 v = 5`
⇒`(9u+4v)/6 = 5`
⇒9u + 4v = 30 …….(iv)
On multiplying (iii) by 4 and (iv) by 3, we get:
20u - 12v = 4 ……..(v)
27u + 12v = 90 ……..(vi)
On adding (iv) and (v), we get:
47u = 94 ⇒ u = 2
⇒`1/x = 2 ⇒ x = 1/2`
On substituting x = 12 in (i), we get:
`5/(1⁄2) - 3/y = 1`
`⇒10 - 3/y = 1 ⇒ 3/y= (10 – 1) = 9`
`y = 3/9 = 1/3`
Hence, the required solution is x = `1/2 and y = 1/3`.
APPEARS IN
संबंधित प्रश्न
For what value of k, the following system of equations will represent the coincident lines?
x + 2y + 7 = 0
2x + ky + 14 = 0
Find the values of a and b for which the following system of equations has infinitely many solutions:
(a - 1)x + 3y = 2
6x + (1 + 2b)y = 6
Solve for x and y:
4x + 6y = 3xy, 8x + 9y = 5xy
Solve for x and y:
`a^2x + b^2y = c^2, b^2x + a^2y = d^2`
Solve for x and y:
`x/a + y/b = a + b, x/(a^2)+ y/(b^2) = 2`
A number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.
The sum of two numbers is 1/6 and the sum of their reciprocals is `1/3`. Find the numbers.
Abdul travelled 300 km by train and 200 km by taxi taking 5 hours and 30 minutes. But, if he travels 260km by train and 240km by taxi, he takes 6 minutes longer. Find the speed of the train and that of taxi.
A chemist has one solution containing 50% acid and a second one containing 25% acid. How much of each should be used to make 10 litres of a 40% acid solution?
Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:
2x + 3y – 5 = 0 and px – 6y – 8 = 0,
if the pair of equations has a unique solution.
