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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.

NCERT Solutions for Class 10 Maths Chapter 3 by Swiflearn are by far the best and most reliable NCERT Solutions that you can find on the internet. These NCERT Solutions for Class 10 Maths Chapter 3 are designed as per the CBSE Class 10th Maths Syllabus. These NCERT Solutions will surely make your learning convenient & fun. Students can also Download FREE PDF of NCERT Solutions Class 10 Chapter 3.

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

NCERT 10th Maths Ch 3 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

NCERT 10th Maths Ch 3 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: