Home
Class 10
MATHS
Solve : (4)/(x)+(5)/(y)=7, (3)/(x)+(4)/(...

Solve : `(4)/(x)+(5)/(y)=7`, `(3)/(x)+(4)/(y)=(11)/(2)`.

Text Solution

Verified by Experts

`{:((4)/(x)+(5)/(y)=7....(1),(3)/(x)+(4)/(y)=(11)/(2)....(2)):}`
Substituting `m` for `(1)/(x)` and `n` for `(1)/(y)`, we get,
`4m+5n=7`………….`(3)`
`{:(3m+4n=(11)/(2), :. 6m+8n=11............(4)):}`
Multiplying equation `(3)` by `3` and equation `(4)` by `2`.
`{:(12m+15n=21" ...(5)"),(12m+16n=-22" ...(6)"),("- - -"),(bar(" "-" "n""="-1)):}` ..........[Substracting equation `(6)` from equation `(5)`]
`:.n=1`
Substituting `n=1` is equation `(3)`,
`{:(4m+5(1)=7, :.4m+5=7, :. 4m=7-5):}`
`{:( :.4m=2, :.m=(1)/(2)):}`.
Resubtituting the values of `m` and `n`.
`{:(m=(1)/(x)=(1)/(2), :.x=2):}`
`{:(n=(1)/(y)=1, :.y=1):}`
Promotional Banner

Topper's Solved these Questions

  • LINEAR EQUATIONS IN TWO VARIABLES

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Assignment 1.4|9 Videos

  • LINEAR EQUATIONS IN TWO VARIABLES

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Practice set 1.1|9 Videos

  • LINEAR EQUATIONS IN TWO VARIABLES

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Assignment 1.3|10 Videos

  • GEOMETRIC CONSTRUCTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise CHALLENGING QUESTION|4 Videos

  • MENSURATION

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Assignment 8.5|8 Videos

Similar Questions

Explore conceptually related problems

(4)/(x)+5y=7 and (3)/(x)+4y=5

Solve the pair of equations : (3)/(x) + (2)/(y) = 7 (5)/(x) - (4)/(y) = 13 Hence find the value of 27x - 12y .

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

Solve (x+2)/(y+2)+2=0,(x-4)/(y-2)=(x-1)/(y+7)

solve for x,y, the following equation (2)/(x)+(3)/(y)=13;(5)/(x)-(4)/(y)=-2

If x:y=1:1, then (3x+4y)/(5x+6y)=(7)/(11) (b) (17)/(11)(17)/(23)(d)(4)/(5)

Solve for x and y: 4/x+5y=7,3/x+4y=5

Solve for x and y : x+(y)/(4)=11," "(5x)/(6)-(y)/(3)=7