Ex 3.1, 1 (i) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

Transcript

Ex 3.1, 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