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, βSeven 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.β (Isnβt 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 = π₯ β 7 years
Seven years ago, daughterβs age = π¦ β 7 years
As per the given condition,
(π₯ β 7) = 7(π¦ β 7)
π₯ β 7 = 7y β 49
x β 7y = β42 β¦β¦(i)
Three years later, Age of Aftab = π₯ + 3 years
Age of daughter = π¦ + 3 years
As per the given condition,
(π₯ + 3) = 3(π¦ + 3)
π₯ + 3 = 3π¦ + 9
π₯ β 3π¦ = 6 β¦β¦ (ii)
Hence, equation (i) and (ii) represent given conditions algebraically as:
π₯ β 7π¦ = β42
π₯ β 3π¦ = 6
Graphical Representation is:
x β 7y = β42
x = β42 + 7y
Solution table is:
For x β 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 βΉ 3900. Later, she
buys another bat and 3 more balls of the same kind for βΉ 1300. Represent
this situation algebraically and geometrically.
Solution:
Let the price of a bat be βΉ x and a ball be βΉ 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 βΉ
160. After a month, the cost of 4 kg of apples and 2 kg of grapes is βΉ 300.
Represent the situation algebraically and geometrically.
Solution:
Let the cost of 1 kg of apples be βΉ π₯ and 1 kg grapes be βΉ y.
The given conditions can be algebraically represented as:
2π₯ + π¦ = 160 β¦ (1)
4π₯ + 2π¦ = 300 β¦ (2)
2π₯ + π¦ = 160
For π¦ = 160 β 2π₯
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 βΉ 50, whereas 7 pencils and 5 pens
together cost βΉ 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
π₯ + π¦ = 10 β¦ (1)
According to question, Number of girls is 4 more than number of boys, so
π₯ = π¦ +4 β¦ (2)
For π₯ + π¦ = 10
π₯ = 10 β π¦
Solution for this equation:
For π₯ = π¦ +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 βΉ π₯ and one pen be βΉ π¦ respectively.
As per the given conditions,
5π₯ + 7π¦ = 50 β¦..(1)
7 π₯ + 5 π¦ = 46 β¦.. (2)
For 5 π₯ + 7 π¦ = 50
π₯ = 50β7y/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