Advertisements
Advertisements
प्रश्न
Solve for x and y:
`10/(x+y) + 2/(x−y) = 4, 15/(x+y) - 9/(x−y) = -2, where x ≠ y, x ≠ -y.`
उत्तर
The given equations are
`10/(x+y) + 2/(x−y) = 4 ` ……(i)
`15/(x+y) - 9/(x−y) = -2` ……(ii)
Substituting `1/(x+y) = u and 1/(x−y)` = v in (i) and (ii), we get:
10u + 2v = 4 ……..(iii)
15u - 9v = -2 …….(iv)
Multiplying (iii) by 9 and (iv) by 2 and adding, we get:
90u + 30u = 36 –4
⇒120u = 32
`⇒u = 32/120 = 4/15`
`⇒x + y = 15/4 (∵1/(x+y)=u)` …..(v)
On substituting u = `4/15` in (iii), we get:
`10 × 4/15 + 2v = 4`
`8/3 + 2v = 4`
⇒2v = 4 - 83 = 43
`⇒v = 2/3`
`⇒ x – y = 3/2 (∵1/(x−y) =v) ` …..(vi)
Adding (v) and (vi), we get
`2x = 15/4 + 3/2 ⇒2x = 21/4 ⇒x = 21/8`
Substituting x` = 21/8 `in (v), we have
`21/8 + y = 15/4 ⇒y = 15/4 - 21/8 = 9/8`
Hence, x =` 21/8 and y =9/8.`
APPEARS IN
संबंधित प्रश्न
For what value of α, the system of equations
αx + 3y = α - 3
12x + αy = α
will have no solution?
Solve for x and y:
`2x + 5y = 8/3, 3x - 2y = 5/6`
Solve for x and y:
`x/a - y/b = 0, ax + by = a^2 + b^2`
Find the values of a and b for which the system of linear equations has an infinite number of solutions:
(2a – 1) x + 3y = 5, 3x + (b – 1)y = 2.
A man invested an amount at 10% per annum simple interest and another amount at 10% per annum simple interest. He received an annual interest of Rs. 1350. But, if he had interchanged the amounts invested, he would have received Rs. 45 less. What amounts did he invest at different rates?
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 .
The length of a room exceeds its breadth by 3 meters. If the length is increased by 3 meters and the breadth is decreased by 2 meters, the area remains the same. Find the length and the breadth of the room.
A railway half ticket costs half the full fare and the reservation charge is the some on half ticket as on full ticket. One reserved first class ticket from Mumbai to Delhi costs ₹4150 while one full and one half reserved first class ticket cost ₹ 6255. What is the basic first class full fare and what is the reservation charge?
If twice the son’s age in years is added to the mother’s age, the sum is 70 years. But, if twice the mother’s age is added to the son’s age, the sum is 95 years. Find the age of the mother and that of the son.
Find the value of k for which the system of equations x + 2y – 3 = 0 and 5x + ky + 7 = 0 is inconsistent.
