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

Ex 3.4, 2 - Form linear equation - If we add 1 to numerator - Elimination

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

Transcript

Ex 3.4, 2 Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction? Let numerator be x and denominator be y So, fraction is ๐‘ฅ/๐‘ฆ Given that, if 1 is added to numerator and 1 is subtracted from the denominator, fraction becomes 1. (๐‘๐‘ข๐‘›๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘œ๐‘Ÿ + 1)/(๐ท๐‘’๐‘›๐‘œ๐‘š๐‘–๐‘›๐‘Ž๐‘ก๐‘œ๐‘Ÿ โˆ’1)=1 (๐‘ฅ + 1)/(๐‘ฆ โˆ’ 1)=1 (x + 1) = (y โ€“ 1) x โ€“ y = โ€“ 1 โ€“ 1 x โ€“ y = โ€“ 2 Also, if we add 1 to the denominator, fraction becomes 1/2. ๐‘๐‘ข๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘œ๐‘Ÿ/(๐ท๐‘’๐‘›๐‘œ๐‘š๐‘–๐‘›๐‘Ž๐‘ก๐‘œ๐‘Ÿ + 1)=1/2 ๐‘ฅ/(๐‘ฆ +1)=1/2 2x = y + 1 2x โ€“ y = 1 Hence, our equations are x โ€“ y = โ€“2 โ€ฆ(1) 2x โ€“ y = 1 โ€ฆ(2) We use elimination method with equation (1) & (2) โ€“x = โ€“3 x = 3 Putting x = 3 in equation (1) x โ€“ y = โ€“2 3 โ€“ y = โ€“2 โ€“y = โ€“ 2 โ€“ 3 โ€“y = โ€“5 y = 5 So, x = 3, y = 5 is the solution of our equation So, x = 3, y = 5 is the solution of our equation โˆด Numerator = x = 3 & Denominator = y = 5 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=3/5

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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.