# CBSE Class 10-Mathematics: Chapter – 3 Pair of Linear Equation in Two Variables Part 13 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 2**:

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 ₹ 50, whereas 7 pencils and 5 pens together cost ₹ 46. Find the cost of one pencil and that of one pen.

**Answer**:

(i) Let number of boys who took part in the quiz

Let number of girls who took part in the quiz

According to given conditions, we have

And

For equation , we have following points which lie on the line

For equation , we have following points which lie on the line

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

We can clearly see that the intersection point of two lines is

Therefore, number of boys who took park in the quiz and, number of girls who took part in the quiz = .

(ii) Let cost of one pencil ₹ and Let cost of one pen ₹

According to given conditions, we have

(1)

(2)

For equation , we have following points which lie on the line

For equation , we have following points which lie on the line

We can clearly see that the intersection point of two lines is .

Therefore, cost of pencil = ₹ 3 and, cost of pen