Learn all Concepts of Chapter 3 Class 10 (with VIDEOS). Check - Linear Equations in 2 Variables - Class 10

 

 

  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
  2. Serial order wise

Transcript

Ex 3.3 ,3 Form the pair of linear equations for the following problems and find their solution by substitution method. (v) 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. Let numerator be x and denominator be y So, fraction is ๐‘ฅ/๐‘ฆ Given that if 2 is added to both the numerator and the denominator, fraction becomes 9/11. (๐‘๐‘ข๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘œ๐‘Ÿ + 2)/(๐ท๐‘’๐‘›๐‘œ๐‘š๐‘–๐‘›๐‘Ž๐‘ก๐‘œ๐‘Ÿ + 2)=9/11 (๐‘ฅ + 2)/(๐‘ฆ + 2)=9/11 11(x + 2) = 9(y + 2) 11x + 22 = 9y + 18 11x โ€“ 9y + 22 โ€“ 18 = 0 11x โ€“ 9y + 4 = 0 Also, given that if 3 is added to both the numerator and the denominator, fraction becomes 5/6. (๐‘๐‘ข๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘œ๐‘Ÿ + 3)/(๐ท๐‘’๐‘›๐‘œ๐‘š๐‘–๐‘›๐‘Ž๐‘ก๐‘œ๐‘Ÿ + 3)=5/6 (๐‘ฅ + 3)/(๐‘ฆ + 3)=5/6 6(x + 3) = 5(y + 3) 6(x + 3) = 5(y + 3) 6x + 18 = 5y + 15 6x โ€“ 5y + 18 โ€“ 15 = 0 6x โ€“ 5y + 3 = 0 Hence, our equations are 11x โ€“ 9y + 4 = 0 โ€ฆ(1) 6x โ€“ 5y + 3 = 0 โ€ฆ(2) From (1) 11x โ€“ 9y + 4 = 0 11x = 9y โ€“ 4 x = ((9๐‘ฆ โˆ’ 4)/11) Putting x in (2) 6x โ€“ 5y + 3 = 0 6 ((9๐‘ฆ โˆ’ 4)/11) โ€“ 5y + 3 = 0 Multiply both sides by 11 11 ร—(6 (9๐‘ฆโˆ’4))/11โˆ’5๐‘ฆร—11+3ร—11=0ร—11 6(9y โ€“ 4 ) โ€“ 55y + 33 = 0 6(9y) โ€“ 6(4) โ€“ 55y + 33 = 0 54y โ€“ 24 โ€“ 55y + 33 = 0 โ€“ y + 9 = 0 โ€“ y = โ€“9 y = 9 Putting y = 9 in (1) 11x โ€“ 9y + 4 = 0 11x โ€“ 9(9) + 4 = 0 11x โ€“ 81 + 4 = 0 11x โ€“ 77 = 0 11x = 77 x = 77/11 x = 7 Therefore x = 7, y = 9 So, Numerator = x = 7 Denominator = y = 9 Hence, original fraction = ๐‘๐‘ข๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘œ๐‘Ÿ/๐ท๐‘’๐‘›๐‘œ๐‘š๐‘–๐‘›๐‘Ž๐‘ก๐‘œ๐‘Ÿ "= " ๐‘ฅ/๐‘ฆ=7/9

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.