NCERT Solutions for Class 10 Maths Chapter 3
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
