Exercise 3.2
Q1. Form the pair of linear equations in the following problems, and 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.
Solution:
Let the numbers of girls be x.
And the number of girls is y.
According to question
The total numbers of boys and girls is 10.
∴ x + y = 10 ……………….. (i)
There are 4 more girls than boys.
∴ x – y = 4 ……………….. (ii)
Table for equation (i)
Graph for these tables will be as follow -
(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.
Solution:
Q5. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
Solution: Let the length of rectangular garden be x m.
And breadth = y m
Semi-perimeter = 36 m
Q6. Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) Intersecting lines
(ii) parallel lines
(iii) Coincident lines
Q7. Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.