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

Last updated at July 27, 2020 by Teachoo

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

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 ๐ฅ/๐ฆ Given that if 2 is added to both the numerator and the denominator, fraction becomes 9/11. (๐๐ข๐๐๐๐๐ก๐๐ + 2)/(๐ท๐๐๐๐๐๐๐๐ก๐๐ + 2)=9/11 (๐ฅ + 2)/(๐ฆ + 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. (๐๐ข๐๐๐๐๐ก๐๐ + 3)/(๐ท๐๐๐๐๐๐๐๐ก๐๐ + 3)=5/6 (๐ฅ + 3)/(๐ฆ + 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 โฆ(1) 6x โ 5y + 3 = 0 โฆ(2) From (1) 11x โ 9y + 4 = 0 11x = 9y โ 4 x = ((9๐ฆ โ 4)/11) Putting x in (2) 6x โ 5y + 3 = 0 6 ((9๐ฆ โ 4)/11) โ 5y + 3 = 0 Multiply both sides by 11 11 ร(6 (9๐ฆโ4))/11โ5๐ฆร11+3ร11=0ร11 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 = โ9 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 = ๐๐ข๐๐๐๐๐ก๐๐/๐ท๐๐๐๐๐๐๐๐ก๐๐ "= " ๐ฅ/๐ฆ=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.