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) Let us assume the number of boys = x

The number of girls = y

Two linear equations can be formed for the given situation.

Total number of boys and girls is represented as:

x + y = 10

Number of girls is 4 more than the number of boys. This can be mathematically represented as:

y = x + 4

-x + y = 4

The algebraic representation where x and y are the numbers of boys and girls respectively are shown below:

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 tabulate these solutions as shown below.

The graphical representation is as follows.

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

Thus,

Number of boys = 3

Number of girls = 7

(ii)  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 given situation.

The cost of 5 pencils and 7 pens is ₹ 50. Mathematically it can be represented as,

5x + 7y = 50

And, the cost of 7 pencils and 5 pens is ₹ 46. Mathematically it can be represented as,

7x + 5y = 46

Thus, the algebraic representation where x and y are the cost of 1 pencil and 1 pen respectively are as follows:

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

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

Therefore, the algebraic representation for equation(1) is:

5x + 7y = 50

7y = 50 - 5x

y = (50 - 5x)/7

And, the algebraic representation for equation(2) is:

7x + 5y = 46

5y = 46 - 7x

y = (46 - 7x)/5

Let us represent these equations graphically. For this, we need at least two solutions for each equation. We will tabulate the solutions as shown below.

The graphical representation is as follows.

From the graph, the solution is ( x, y) = (3, 5)

Therefore,

Cost of one pencil = ₹ 3

Cost of one pen = ₹ 5

☛ Check: NCERT Solutions Class 10 Maths Chapter 3

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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

Summary:

The pair of linear equations in the following problems are formed and their solutions are found 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, upon solving the questions with the help of graph, number of boys = 3 and number of girls = 7. (ii) 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.

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