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.

(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.

(i) Let number of boys = x

Let number of girls = y

According to the question,

=

=

Putting y = 0 , 5, 10 . we get,

X = 10 – 0 = 10

X = 10 – 5 = 5

X = 10 – 10 = 0

Number of girls is 4 more than number of boys …………Given

So,

Y = x + 4

Putting x = -4 ,0 , 4 we get,

Y = -4+4 = 0

Y= 0 + 4 = 4

Y = 4 + 4 = 8

Graphical representation :

(ii) Let cost of one pencil = Rs. X

Let cost of one pen = Rs. Y

According to the question,

=

=

=

Putting value of y = 5 , 10 , 15 we get,

X =

X =

X =

Now,

7 pencils and 5 pens together cost Rs. 46

7x + 5y = 46

= 5y = 46 – 7x

= y = 9.2 – 1.4x

Putting x = 0 , 2 , 4 we get,

Y= 9.2 – 1.4×0 = 9.2

Y = 9.2 – 1.4 × 2 = 9.2 – 2.8 = 6.4

Y = 9.2 – 1.4 × 4 = 9.2 – 5.6 = 3.6

Graphical Representation: