CBSE Notes Class 9 Maths Chapter 4 Linear Equations in Two Variables

1.0Introduction to Linear Equations in Two Variables

In Math, a Linear Equations in Two Variables is an equation with the highest power equal to 1. When this kind of equation consists of two variables, let’s say x and y, it is said to be a linear equation of two variables. The general form of this kind of equation is:

a x + b y = c 

Here, a, b, and c are the constant. While x and y are variables.

2.0Download CBSE Class 9 Maths Notes Chapter 4 Linear Equations in Two Variables - Free PDF

Mastering Linear Equations in Two Variables is now easier with our free, student-friendly CBSE Notes Class 9 Maths Chapter 4 PDF. These notes are crafted to provide complete clarity on topics such as standard form of linear equations, graph plotting, and solution sets.

3.0CBSE Class 9 Maths Chapter 4 Linear Equation in Two Variables - Revision Notes

What are Linear Equations? 

Linear equations are named so because when these equations are plotted to a graph or cartesian plan, they form the shape of a line. For example:

$5\mathrm{x}=0,6\mathrm{x}+9\mathrm{y}=0\text{, or }\mathrm{y}=\frac{1}{3}x+9$.

Constructing Equations Based On Word Problems

Making equations from word problems involves translating a situation or relationship described in words into a mathematical equation. You will identify the variable, give data, and the relationship between quantities. Given this information, you can formulate a linear equation to represent the situation that can be solved to find the unknown values. 

For Example: In a cricket match, two batters, namely Virat Kohli and Shubman Gill, scored 200 runs combined. How will you represent this situation in maths?

Solution: Let runs scored by Virat Kohli = x 

Let runs scored by Shubman Gill = y 

According to the question,

x + y = 200

Linear Equation in Two Variables Solutions 

• The solution of a linear equation in two variables is any ordered pair (x,y) that satisfies the equations. 
• Since we have two variables, the solutions for these types of equations are infinite. 

Finding the Solutions:

Step 1: Convert the equation (if not already) to Standard form. That is: 

a x + b y = c

Step 2: Use the hit and trial method and put various values for x and y. 

Step 3: By putting the value of x or y, you will get the ordered pair of (x,y). These values are called the solutions of any equation. 

Also Read: Linear Equation in One Variable

4.0Solved Problems

Question 1: Find the value of k in the given equation kx + 9y = 18 if x = 2 and y = 1 

Solution: put x = 2 and y = 1 in the given equation. 

$k\times 2+9\times 1=18$

$2\mathrm{k}=9$

$\mathrm{K}=4.5$

Question 2: write at least 3 solutions of the given equation. 

1. 4 x+9 y=24
2. 6 x+7 y=21

Solution(A): 4x+9y=24 

B) 6x+7y=21 

Question 3: In a stationery shop a salesman sells a drawing book that is thrice the cost of a pen. Construct a linear equation based on the following information. 

Solution: 

Let the price of the drawing book = x

Let the price of the pen = y 

According to the question, 

x = 3y 

x - 3y = 0 

5.0Key Features of CBSE Maths Notes for Class 9 Chapter 4

• Clear Concept Introduction – Explains what a linear equation in two variables is, its standard form (ax + by + c = 0), and meaning of variables using simple language suitable for beginners.
• Understanding Ordered Pairs & Solutions – Shows how ordered pairs satisfy an equation and how infinitely many solutions are possible.
• Consistency & Nature of Graphs – Helps students understand how different equations represent parallel, intersecting, or coincident lines (basic conceptual exposure).
• NCERT Based Solved Examples – Step-by-step textbook solutions aligned with the CBSE exam pattern.
• CBSE Syllabus Coverage – Designed according to the latest CBSE curriculum, making it useful for school exams and foundational algebra learning.