# 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

**Solution:**

(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.

Let us Assume, the number of boys = x.

The number of girls = y.

The two linear equations can be formed for the above situation.

Total number of boys and girls is:

x + y = 10

Number of girls is 4 more than the number of boys, Mathematically:

y = x + 4

-x + y = 4

Algebraic representation where x and y are the number of boys and girls respectively.

x + y = 10 ....(1)

-x + y = 4 ....(2)

Therefore, the algebraic representation for equation 1 is:

x + y = 10

y = 10 - x

And, the algebraic representation is for equation 2 is:

-x + y = 4

y = x + 4

Let us represent these equations graphically. For this, we need at least two solutions for each equation. We give these solutions in the table shown below.

The graphical representation is as follows.

From graph solution ( x, y) = (3, 7)

Number of boys = 3

Number of girls = 7

(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.

Assuming the cost of 1 pencil as ₹ x and the cost of 1 pen as ₹ y, two linear equations are to be formed for the above situation.

The cost of 5 pencils and 7 pens is ₹ 50. Mathematically,

5x + 7 y = 50

And, the cost of 7 pencils and 5 pens is ₹ 50. Mathematically,

7x + 5y = 46

Algebraic representation where x and y are the cost of 1 pencil and 1 pen respectively.

5x + 7 y = 50 ....(1)

7x + 5y = 46 ....(2)

Therefore, the algebraic representation for equation 1 is:

5x + 7 y = 50

7 y = 50 - 5x

y = (50 - 5x)/7

And, the algebraic representation for equation 2 is:

7 x + 5 y = 46

5 y = 46 - 7x

y = (46 - 7x)/5

Let us represent these equations graphically. For this, we need at least two solutions for each equation. We give these solutions in table shown below.

The graphical representation is as follows.

From graph Solution ( x, y) = (3, 5)

Cost of one pencil = ₹ 3

Cost of one pen = ₹ 5

**Video Solution:**

## 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

### NCERT Solutions for Class 10 Maths - Chapter 3 Exercise 3.2 Question 1:

10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, upon solving the questions with the help of graph, no. of boys = 3 and no. of girls = 7. 5 pencils and 7 pens together cost ₹ 50, whereas 7 pencils and 5 pens together cost ₹ 46, hence, upon solving with the help of graph we can say that cost of one pencil = ₹ 3 and cost of one pen = ₹ 5.