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

Last updated at May 3, 2020 by Teachoo

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

Transcript

Ex 3.5,4 Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method : (ii) A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction Let numerator be x and denominator be y So, fraction is ๐ฅ/๐ฆ Given that, if 1 is subtracted from numerator fraction becomes 1/3. (๐๐ข๐๐๐๐๐ก๐๐ โ1)/(๐ท๐๐๐๐๐๐๐๐ก๐๐ )=1/3 (๐ฅ โ 1)/(๐ฆ )=1/3 3(x โ 1) = 1(y) 3x โ 3 = y 3x โ y = 3 Also, if 8 is added to the denominator, fraction becomes 1/4. (๐๐ข๐๐๐๐๐ก๐๐ )/(๐ท๐๐๐๐๐๐๐๐ก๐๐ + 8)=1/4 (๐ฅ )/(๐ฆ + 8)=1/4 4(x) = 1(y + 8) 4x = y + 8 4x โ y = 8 From (1) 3x โ y = 3 3x = y + 3 x = ((๐ฆ + 3)/3) Putting value of x in (2) 4x โ y โ 8 = 0 4 ((๐ฆ + 3)/3 ) โ y โ 8 = 0 Multiplying the equation by 3 3 ร"4 (" (๐ฆ + 3)/3 ")"โ3ร๐ฆโ3ร8=0ร8 4(y + 3 ) โ 3y โ 24 = 0 4y + 12 โ 3y โ 24 = 0 4y โ 3y โ 24 + 12 = 0 y โ 12 = 0 y = 12 Putting y = 12 in equation (1) 3x โ y = 3 3x โ 12 = 3 3x = 12 + 3 3x = 15 x = 15/3 x = 5 Therefore x = 5, y = 12 is the solution So, Numerator = x = 5 Denominator = y = 12 Hence, original fraction = ๐๐ข๐๐๐๐๐ก๐๐/๐ท๐๐๐๐๐๐๐๐ก๐๐ "= " ๐ฅ/๐ฆ=5/12

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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.