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

Last updated at Dec. 18, 2020 by Teachoo

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

Transcript

Ex 3.2, 1 Form the pair of linear equations in the following problems & find their solutions graphically (i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. Let Number of Girls who took part in the quiz be x & Number of Boys who took part in the quiz be y Given Total 10 students took part in the quiz ∴ Number of girls + Number of boys = 10 x + y = 10 Also, Number of girls is 4 more than boys Number of girls = 4 + Number of boys x = 4 + y x – y = 4 Now, plotting equations x + y = 10 ...(1) x − y = 4 …(2) For Equation (1) x + y = 10 Putting x = 4 4 + y = 10 y = 10 − 4 y = 6 So, x = 4, y = 6 is a solution i.e. (4, 6) is a solution Putting y = 4 x + 4 = 10 x = 10 − 4 x = 6 So, x = 6, y = 4 is a solution i.e. (6, 4) is a solution For Equation (2) x − y = 4 Putting y = 0 x − 0 = 4 x = 4 So, x = 4, y = 0 is a solution i.e. (4, 0) is a solution Putting x = 6 6 − y = 4 6 − 4 = y y = 2 So, x = 6, y = 2 is a solution i.e. (6, 2) is a solution We will plot both equations on the graph Therefore, Solution of the equations is (7, 3) Thus, Number of girls in the quiz competition = x = 7 Number of boys in the quiz competition = y = 3 Ex 3.2, 1 Form the pair of linear equations in the following problems & find their solutions graphically (ii) 5 pencils and 7 pens together cost Rs. 50 , whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen Let the Cost of one Pencil be Rs x & Cost of one Pen be Rs y Given that 5 pencils and 7 pens together cost Rs 50 5 × (Cost of pencil) + 7 × (Cost of pens) = 50 5x + 7y = 50 Also, 7 pencils and 5 pens together cost Rs. 46 7 × (Cost of pencil) + 5 × (Cost of pen) = 46 7x + 5y = 46 Now, plotting equations 5x + 7y = 50 ...(1) 7x + 5y = 46 …(2) For Equation (1) 5x + 7y = 50 Let y = 5 5x + 7(5) = 50 5x + 35 = 50 5x + 35 = 50 − 35 5x = 15 x = 15/5 x = 3 So, x = 3, y = 5 is a solution i.e. (3, 5) is a solution Let x = 0 5(0) + 7y = 50 7y = 50 y = 50/7 y = 7.14 So, x = 0, y = 7.14 is a solution i.e. (0, 7.14) is a solution For Equation (2) 7x + 5y = 46 Let y = 0 7x + 5(0) = 46 7x = 46 x = 46/7 x = 6.57 So, x = 6.57, y = 0 is a solution i.e. (6.57, 0) is a solution Let x = 3 7(3) + 5y = 46 21 + 5y = 46 5y = 46 − 21 5y = 25 y = 25/5 y = 5 So, x = 3, y = 5 is a solution i.e. (3, 5) is a solution We will plot both equations on the graph Therefore, Solution of the equations is (3, 5) Thus, Cost of 1 Pencil = x = Rs 3 Cost of 1 Pen = y = Rs 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.