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.
Mastering Linear Equations in Two Variables is now easier with our free, student-friendly CBSE Notes Class 9 Maths Chapter 4. These notes are crafted to provide complete clarity on topics such as standard form of linear equations, graph plotting, and solution sets.
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:
.
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
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.
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.
Question 2: write at least 3 solutions of the given equation.
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
(Session 2025 - 26)