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 (i)**

Let number of boys who took part in the quiz = x

Let number of girls who took part in the quiz = y

**According to given conditions, we have**

**(1)**

And, ** **

** (2)**

So, we have equations **(1)** and **(2),**

To represent them graphically, we will find 3 sets of points which lie on the lines. Point of intersection of two lines would be the solution.

We plot the points for both of the equations to find the solution.

**(Blue)** and **(Red)**

We can clearly see that the intersection point of two lines is **(3, 7).**

Therefore, number of boys who took park in the quiz = 3

And, number of girls who took part in the quiz = 7

**(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 cost of one pencil = Rs x

Let cost of one pen = Rs y

**According to given conditions, we have**

**(1)**

** (2)**

So, we have equations **(1)** and **(2),**

To represent them graphically, we will find 3 sets of points which lie on the lines. Point of intersection of two lines would be the solution.

**(Blue)** and **(Red)**

We can clearly see that the intersection point of two lines is **(3, 5).**

Therefore, cost of pencil = Rs 3

And, cost of pen = Rs 5