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 3.4 ,2 Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number. Number is of the form Let digit at units place = y and the digit at tens place = x Given that sum of digits of two digit number is 9 ∴ Digit at tens place + Digit at units place = 9 x + y = 9 It is given 9 times the number is twice the number obtained by reversing the digits 9 × (Number) = 2 × (Reversed number) 9 (10x + y) = 2 (10y + x) 90x + 9y = 20 y + 2x 90x – 2x + 9y – 20y = 0 88x – 11 y = 0 11(8x – y) = 0 (8x – y) = 0/11 (8x – y) = 0 8x – y = 0 Hence, our equations are x + y = 9 …(1) 8x – y = 0 …(2) We use elimination method with equation (1) & (2) 9x = 9 x = 9/9 ∴ x = 1 Putting x = 1 in (1) x + y = 9 1 + y = 9 y = 9 – 1 y = 8 So, x = 1, y = 8 is the solution of our equation ∴ Digit at units place = y = 8 & digit at tens place = x = 1 Therefore, Number = 10x + y = 10(1) + 8 = 10 + 8 = 18 So, the required number is 18

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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.