NCERT Class 10 Maths Chapter 3 is Pair of Linear Equations in Two Variables that has 7 exercises. Important topics are graphical representations, Algebraic methods for solving longer equations, substitution method, elimination method, equations reducible to linear equations, and cross-multiplication methods.

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## NCERT Solutions for Class 10 Maths Chapter 3 : Pair of Linear Equations in Two Variables EX 3.1

**Question 1:**

**Aftab tells his daughter, “Seven years ago, I was seven times as old as you**

**were then. Also, three years from now, I shall be three times as old as you**

**will be.” (Isn’t this interesting?) Represent this situation algebraically and**

**graphically.**

**Solution**:

Let the present age of Aftab be x years.

Let present age of daughter be y years.

Seven years ago, Age of Aftab = 𝑥 − 7 years

Seven years ago, daughter’s age = 𝑦 − 7 years

As per the given condition,

(𝑥 − 7) = 7(𝑦 − 7)

𝑥 − 7 = 7y − 49

x − 7y = −42 ……(i)

Three years later, Age of Aftab = 𝑥 + 3 years

Age of daughter = 𝑦 + 3 years

As per the given condition,

(𝑥 + 3) = 3(𝑦 + 3)

𝑥 + 3 = 3𝑦 + 9

𝑥 − 3𝑦 = 6 …… (ii)

Hence, equation (i) and (ii) represent given conditions algebraically as:

𝑥 − 7𝑦 = −42

𝑥 − 3𝑦 = 6

Graphical Representation is:

x − 7y = −42

x = −42 + 7y

Solution table is:

For x − 3y = 6

x = 6 + 3y

Solution for this equation:

The graphical representation is as follows:

**Question 2.**

**The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she**

**buys another bat and 3 more balls of the same kind for ₹ 1300. Represent**

**this situation algebraically and geometrically.**

**Solution**:

Let the price of a bat be ₹ x and a ball be ₹ y.

According to question

**Question 3. **

**The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹**

**160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹ 300.**

**Represent the situation algebraically and geometrically.**

**Solution**:

Let the cost of 1 kg of apples be ₹ 𝑥 and 1 kg grapes be ₹ y.

The given conditions can be algebraically represented as:

2𝑥 + 𝑦 = 160 … (1)

4𝑥 + 2𝑦 = 300 … (2)

2𝑥 + 𝑦 = 160

For 𝑦 = 160 − 2𝑥

Solution for this equation:

## NCERT Solutions for Class 10 Maths Chapter 3 : Pair of Linear Equations in Two Variables EX 3.2

**Question 1.**

**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 the number of girls in the class be x and number of boys in the class be y.

As per the question, total number of students =10

𝑥 + 𝑦 = 10 … (1)

According to question, Number of girls is 4 more than number of boys, so

𝑥 = 𝑦 +4 … (2)

For 𝑥 + 𝑦 = 10

𝑥 = 10 − 𝑦

Solution for this equation:

For 𝑥 = 𝑦 +4

Solutions for this equation:

The graphical representation is as follows

From the graph, it can be observed that the two lines intersect each other at the point (7, 3).

So, x = 7 and y = 3.

Hence, the number of girls and boys in the class are 7 and 3 respectively.

(ii)

Let the cost of one pencil be ₹ 𝑥 and one pen be ₹ 𝑦 respectively.

As per the given conditions,

5𝑥 + 7𝑦 = 50 …..(1)

7 𝑥 + 5 𝑦 = 46 ….. (2)

For 5 𝑥 + 7 𝑦 = 50

𝑥 = 50−7y/5

Solutions for this equation:

## NCERT Solutions for Class 10 Maths Chapter 3 : Pair of Linear Equations in Two Variables EX 3.3

## NCERT Solutions for Class 10 Maths Chapter 3 : Pair of Linear Equations in Two Variables EX 3.4

## NCERT Solutions for Class 10 Maths Chapter 3 : Pair of Linear Equations in Two Variables EX 3.5

## NCERT Solutions for Class 10 Maths Chapter 3 : Pair of Linear Equations in Two Variables EX 3.6

## NCERT Solutions for Class 10 Maths Chapter 3 : Pair of Linear Equations in Two Variables EX 3.7