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.

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