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 : (v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle. Let length of rectangle be x units And breadth of rectangle be y units Hence, Area = Length × Breadth Area = xy Given that, Area gets reduced by 9 square units, if length is reduced by 5 units and breadth increased by 3 units and Area increase by 67 square units, if length is increased by 3 units and breadth increased by 2 units (x – 5) (y + 3) = xy – 9 x (y + 3) – 5 (y + 3) = xy – 9 x (y + 3) – 5 (y + 3) = xy – 9 xy + 3x – 5y - 15 = xy – 9 xy + 3x – 5y - 15 - xy + 9 = 0 3x – 5y – 6 = 0 (x + 3) (y + 2) = xy + 67 x(y + 2) + 3(y + 2) = xy + 67 xy + 2x + 3y + 6 = xy + 67 xy + 2x + 3y + 6 - xy – 67 = 0 2x + 3y – 61 = 0 Hence, our equations are 3x – 5y – 6 = 0 …(1) 2x + 3y – 61 = 0 …(2) From (1) 3x – 5y – 6 = 0 3x = 6 + 5y x = (6 + 5𝑦)/3 Putting value of x in (2) 2x + 3y – 61 = 0 2((6 + 5𝑦)/3) + 3y – 61 = 0 Multiplying both sides by 3 3 × 2(((6+5𝑦))/3) + 3 × 3y – 3 × 61 = 0 2(6 + 5y) + 9y – 183 = 0 12 + 10y + 9y - 183 = 0 19y – 171 = 0 19y = 171 y = 171/19 y = 9 Putting y = 9 in equation (1) 3x – 5y – 6 = 0 3x – 5(9) – 6 = 0 3x – 45 – 6 = 0 3x – 51 = 0 3x = 51 x = 51/3 x = 17 Therefore x = 17, y = 9 is the solution Hence, Length of rectangle = x = 17 units Breadth of rectangle = y = 9 units

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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.