Home
Class 10
MATHS
1/(2x)-1/y=-1 , 1/x+1/(2y)=8...

`1/(2x)-1/y=-1 , 1/x+1/(2y)=8`

Text Solution

Verified by Experts

The given equations are `(1)/(2x) - (1)/(y) = - 1` ….(1)
and `(1)/(x) + (1)/(2y) = 8` …. (2)
Let `(1)/(x) = u` and `(1)/(y) = v` then equation (1) and (2) can be written as
`(u)/(2) - v = - 1`
implies u - 2v = - 2 ….(3)
and `u + (v)/(2) = 8`
implies 2u + v = 16 .... (4)
Multiplying equation (3) by 1 and (4) by 2, we get
u - 2v = - 2. ....(5)
4u + 2v = 32 .... (6)
Adding equations (5) and (6), we get
5u = 30
implies u = 6
Substituting u = 6 in equation (3), we get
6 - 2v = - 2
implies -2v = - 8
implies v = 4
Now, `(1)/(x) = u` implies `(1)/(x) = 6` implies `x = (1)/(6)`
and `(1)/(y) = v` implies `(1)/(y) = 4` implies `y = (1)/(4)`
Hence, the solution is `{:(x = (1)/(6)),(y = (1)/(6)):}}`
Promotional Banner

Topper's Solved these Questions

  • LINEAR EQUATIONS IN TWO VARIABLES

    NAGEEN PRAKASHAN|Exercise Exercise 3a|18 Videos

  • LINEAR EQUATIONS IN TWO VARIABLES

    NAGEEN PRAKASHAN|Exercise Exercise 3b|30 Videos

  • INTRODUCTION TO TRIGONOMETRY

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|5 Videos

  • POLYNOMIALS

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|4 Videos

Similar Questions

Explore conceptually related problems

Find the value of ( 1/x + 1/y ) ( 1/x - 1/y ) ( 1/x^2 + 1/y^2 )

What is the Simplified value of: 1/8 { (x + 1/y)^2 - (x - 1/y)^2}

If 2^(x) = 4^(y) = 8^(z) and xyz = 288 , the value of 1/(2x) + 1/(4y) + 1/(8z) is

(x + 1) / (y) = 1, (x) / (y + 1) = (1) / (2)

The equation of the straight line passing through the point (4,3) and making intercepts on the co-ordinate axes whose sum is -1 is (a) (x)/(2)-(y)/(3)=1 and (x)/(-2)+(y)/(1)=1(x)/(2)-(y)/(3)=-1 and (x)/(-2)+(y)/(1)=-1 (c) (x)/(2)+(y)/(3)=1 and (x)/(2)+(y)/(1)=-1(x)/(2)+(y)/(1)=-1 and (x)/(-2)+(y)/(1)=-1

2x - y gt 1 , x - 2y lt 1

(x+1)/(2)+(y-1)/(3)=8;(x-1)/(3)+(y+1)/(2)=9