Exercise 4.1 from Chapter 4 – Linear Equations in Two Variables, provides you with equations that include two variables that we usually name "x" and "y". Learning this exercise will allow you to know how to see if a given ordered pair of values is a solution for the linear equation. This exercise will also give you an insight into how many solutions can a linear equation have.
These NCERT Solutions are made following the latest NCERT syllabus and each solution is written in simplified steps so you can easily follow the method and the concept behind solving the linear equation.
Through regular practice of this exercise, you will have the foundation needed to attempt and solve word problems and graphing questions in any exercise. This topic will also be useful for higher classes and other competitive exams like Maths Olympiads.
Reading and practicing Exercise 4.1 using the NCERT solutions will make it easier to prepare, feel confident about your writing and scoring higher marks in exams.
Exercise 4.1 of NCERT Solutions for Class 9 Maths Chapter 4 shows you how to verify if a given pair of values solves a linear equation and solve each question in a clear and straightforward way. Download the FREE PDF of the this NCERT from below:
1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
Sol. Let the cost of a pen be Rs. x and that of a notebook be Rs. y. We are given that y=2×x i.e., y=2x. Hence, the required linear equation is y=2x
2. Express the following linear equations in the form ax+by+c=0 and indicate the values of a,b and c in each case :
(i) 2x+3y=9.35
(ii) x−y/5−10=0
(iii) −2x+3y=6
(iv) x=3y
(v) 2x=−5y
(vi) 3x+2=0
(vii) y−2=0
(viii) 5=2x
Sol. (i) 2x+3y−9.35=0
Here, a=2, b=3, c=−9.35
(ii) x−y/5−10=0
i.e., 1x+(−1/5)y+(−10)=0
Here, a=1, b=−1/5, c=−10
(iii) −2x+3y=6
i.e., 2x−3y+6=0,
i.e., 2x+(−3)y+6=0
Here, a=2, b=−3, c=6
(iv) x=3y, i.e., 1x+(−3)y+0=0
Here, a=1, b=−3, c=0
(v) 2x=−5y, i.e., 2x+5y+0=0
Here, a=2, b=5, c=0
(vi) 3x+2=0
i.e. (3)x+(0)y+(2)=0
Here, a=3, b=0 and c=2.
(vii) y−2=0
i.e. (0)x+(1)y+(−2)=0
Here, a=0, b=1 and c=−2.
(viii) 5=2x
=> 5−2x=0
=> −2x+0y+5=0
=> (−2)x+(0)y+(5)=0
Here, a=−2, b=0 and c=5.
This exercise will introduce you to how to check the solutions of equations with two variables.
All questions are following the current NCERT syllabus of Class 9 Maths.
Helps you understand that linear equations can have many perfect possibilities of being resolved, not just one.
Practice of NCERT Solutions will make it easier to answer word problems during examinations and tests.
The step-by-step answers will also help you relieve doubts and prepare effectively for the exam.
Regular revision will build a firm foundation for this section of algebra for higher level classes and competitive examinations.
(Session 2025 - 26)