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
Find the value of k for which each of the following system of equations has infinitely many solutions :
8x + 5y = 9
kx + 10y = 18
Find the value of k for which each of the following system of equations has infinitely many solutions :
2x +3y = k
(k - 1)x + (k + 2)y = 3k
Solve for x and y:
`(bx)/a - (ay)/b + a + b = 0, bx – ay + 2ab = 0`
Solve for x and y:
`x/a + y/b = a + b, x/(a^2)+ y/(b^2) = 2`
Find the values of a and b for which the system of linear equations has an infinite number of solutions:
2x + 3y = 7, 2ax + (a + b)y = 28.
A lady has only 50-paisa coins and 25-paisa coins in her purse. If she has 50 coins in all totaling Rs.19.50, how many coins of each kind does she have?
A number consists of two digits. When it is divided by the sum of its digits, the quotient is 6 with no remainder. When the number is diminished by 9, the digits are reversed. Find the number.
The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3. They are in the ratio of 2: 3. Determine the fraction.
A sailor goes 8 km downstream in 420 minutes and returns in 1 hour. Find the speed of the sailor in still water and the speed of the current .
On selling a tea-set at 5% loss and a lemon-set at 15% gain, a shopkeeper gains Rs. 7. However, if he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains Rs. 14. Find the price of the tea-set and that of the lemon-set paid by the shopkeeper.
