Advertisements
Advertisements
प्रश्न
Solve the following pair of equations:
`4x + 6/y = 15, 6x - 8/y = 14, y ≠ 0`
उत्तर
Given pair of linear equations are
`4x + 6/y` = 15 ......(i)
And `6x - 8/y = 14, y ≠ 0` ....(ii)
Let u = `1/y`, then above equation becomes
4x + 6u = 15 .....(iii)
And 6x – 8u = 14 .....(iv)
On multiplying equation (iii) by 8 and equation (iv) by 6 and then adding both of them, we get
32x + 48u = 120
36x – 48u = 84
⇒ 68x = 204
⇒ x = 3
Now, put the value of x in equation (iii), we get
4 × 3 + 6u = 15
⇒ 6u = 15 – 12
⇒ 6u = 3
⇒ u = `1/2`
⇒ `1/y = 1/2` .....`[because u = 1/y]`
⇒ y = 2
Hence, the required values of x and y are 3 and 2, respectively.
APPEARS IN
संबंधित प्रश्न
A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
A fraction becomes `1/3` when 1 is subtracted from the numerator and it becomes `1/4` when 8 is added to its denominator. Find the fraction.
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Solve the following systems of equations:
`sqrt2x + sqrt3y = 0`
`sqrt3x - sqrt8y = 0`
Solve each of the following systems of equations by the method of cross-multiplication :
`(ax)/b - (by)/a = a + b`
ax - by = 2ab
Solve the following pair of equations:
`1/(2x) - 1/y = -1, 1/x + 1/(2y) = 8, x, y ≠ 0`
Solve the following pair of equations:
`x/a + y/b = a + b, x/a^2 + y/b^2 = 2, a, b ≠ 0`
Find the solution of the pair of equations `x/10 + y/5 - 1` = 0 and `x/8 + y/6` = 15. Hence, find λ, if y = λx + 5.
In a competitive examination, one mark is awarded for each correct answer while `1/2` mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?
For what values of k will the following pair of linear equations have infinitely many solutions?
kx + 3y – (k – 3) = 0
12x + ky – k = 0
