NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.1 are provided here to help students with their Class 10 board exam preparation. These solutions are prepared by experienced subject experts to ensure students understand the basic concepts of linear equations clearly and confidently.
Exercise 3.1 introduces students to the concept of pair of linear equations in two variables and their graphical representation. This exercise helps students understand how two linear equations represent two straight lines on a graph and how their point of intersection represents the solution of the equations. The questions mainly focus on identifying equations, forming linear equations, and understanding their nature.
NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.1
Q.
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.
Q.
The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 2 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.
Q.
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.
Q.
In the given figure, graph of two linear equations are shown. The pair of these linear equations is :
[CBSE - 2024]
NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.1
The solutions are written in a simple, step-by-step manner, strictly following the NCERT guidelines and CBSE exam pattern, helping students build a strong foundation for solving linear equations using graphical and algebraic methods in later exercises.
Q.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.” Represent this situation algebraically and graphically.
Ans:
Let the present age of Aftab and his daughter be x years and y years respectively.
Seven years ago,
Aftab’s age = (x − 7) years
Daughter’s age = (y − 7) years
According to the question,
x − 7 = 7(y − 7)
or
x − 7y + 42 = 0
Three years hence,
Age of Aftab = (x + 3) years
Age of daughter = (y + 3) years
According to the question,
x + 3 = 3(y + 3)
or
x − 3y − 6 = 0
Hence, the given information is represented algebraically by the two equations:
x − 7y + 42 = 0
x − 3y − 6 = 0
To represent these equations graphically, we need at least two solutions for each equation.
For
x − 7y + 42 = 0
or
x = 7y − 42
For
x − 3y − 6 = 0
or
x = 3y + 6
Q.2 The coach of a cricket team buys 3 bats and 6 balls for ₹3900. Later, she buys another bat and 2 more balls of the same kind for ₹1300.
Represent this situation algebraically and geometrically.
Ans:
Let the price of a bat and a ball be ₹x and ₹y respectively.
According to the question,
3x + 6y = 3900 ...(1)
or
3(x + 2y) = 3900
x + 2y = 1300 ...(2)
Equation (1) represents the total price of 3 bats and 6 balls,
Equation (2) represents the total price of one bat and two balls.
For
3x + 6y = 3900
or
y = (3900 − 3x)/6
For
x + 2y = 1300
or
y = (1300 − x)/2
The graphical representation shows that the graphs of both equations coincide.
Q.3 The cost of 2 kg of apples and 1 kg of grapes on a day was ₹160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹300. Represent the situation algebraically and geometrically.
Ans:
Let the price of 1 kg of apples and grapes be ₹x and ₹y respectively.
2x + y = 160 ...(1)
4x + 2y = 300
or
2x + y = 150 ...(2)
For equation (1):
y = 160 − 2x
For equation (2):
y = 150 − 2x
The two lines are parallel and never intersect.
FAQs: Class 10 Maths Chapter 3 – Exercise 3.1
Q1. What is a pair of linear equations in two variables?
Answer:
A pair of linear equations in two variables consists of two equations of the form
a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,
where x and y are variables and a, b, c are real numbers.
Q2. What is the main focus of Exercise 3.1?
Answer:
Exercise 3.1 focuses on understanding linear equations, identifying whether given equations are linear, and forming pairs of linear equations in two variables.
Q3. Are graphs required in Exercise 3.1?
Answer:
No, Exercise 3.1 mainly deals with conceptual understanding and identification of linear equations. Graph-based solving is covered in later exercises.
Q4. Why is this exercise important for Class 10 exams?
Answer:
This exercise builds the foundation for solving linear equations graphically and algebraically, which carries good weightage in board exams.
Q5. How do NCERT Solutions help in exam preparation?
Answer:
NCERT Solutions provide clear explanations and correct methods, helping students avoid common mistakes and gain confidence for board-level questions.