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# Form the pair of linear equations for the following problems and find their solution by substitution method.A fraction becomes 9/11 , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction. Q.3(5)

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Yesterday i am doing this question but it looking tough for me to solve this question how can i easily solve this question Form the pair of linear equations for the following problems and find their solution by substitution method.A fraction becomes 9/11 , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.

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### 2 Answers

1. Let the fraction be x/y.

According to the question,

(x+2) /(y+2) = 9/11

11x + 22 = 9y + 18

11x â€“ 9y = -4 â€¦â€¦â€¦â€¦â€¦.. (1)

(x+3) /(y+3) = 5/6

6x + 18 = 5y +15

6x â€“ 5y = -3 â€¦â€¦â€¦â€¦â€¦â€¦. (2)

From (1), we get x = (-4+9y)/11Â â€¦â€¦â€¦â€¦â€¦.. (3)

Substituting the value of x in (2), we get

6(-4+9y)/11 -5y = -3

-24 + 54y â€“ 55y = -33

-y = -9

y = 9 â€¦â€¦â€¦â€¦â€¦â€¦â€¦ (4)

Substituting the value of y in (3), we get

x = (-4+9Ã—9 )/11 = 7

Hence the fraction is 7/9.

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2. This is the video solution for question 3(v) chapter 3 pair of linear equations in two variables exercise 3.3. Hope you all likes it!!!!

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