Introduction
Linear Equations in Two Variables is an important chapter in Class 9 Mathematics. It helps students understand relationships between two quantities.
For example:
Cost of apples and oranges
Distance and time
Salary and working hours
All these situations can be represented using linear equations.
š For official reference, you can check the NCERT Class 9 Maths textbook.
š¢ What is a Linear Equation in Two Variables?
A linear equation in two variables is an equation of the form:
ax + by + c = 0
Where:
x and y are variables
a, b, c are constants
š Examples of Linear Equations
x + y = 5
2x + 3y = 10
x ā y = 2
š§ Solution of Linear Equation
The solution of a linear equation is any pair of values of x and y that satisfy the equation.
Example:
x + y = 5
Possible solutions:
(1, 4)
(2, 3)
(0, 5)
š Method to Find Solutions
Step 1:
Choose any value of x
Step 2:
Put it in equation
Step 3:
Find value of y
š Graph of Linear Equation
The graph of a linear equation in two variables is always a straight line.
Steps to draw graph:
Make a table of values
Plot points on graph paper
Join the points
āļø Example (Graph Method)
Equation: x + y = 4
x
y
0
4
1
3
2
2
Plot these points and join them ā straight line
š Important Points About Graph
Every linear equation represents a straight line
Infinite solutions lie on the line
Two points are enough to draw a line
š§® Special Cases
- Equation of form x = a
š Vertical line - Equation of form y = b
š Horizontal line
š Real Life Applications
Linear equations are used in:
Business calculations
Budget planning
Physics formulas
Daily life problems
āļø Solved Examples
Q1. Find two solutions of 2x + y = 6
Let x = 1 ā y = 4
Let x = 2 ā y = 2
Q2. Check if (2,3) is a solution of x + y = 5
2 + 3 = 5 ā
Q3. Draw graph of y = 2x
Take values:
x
y
0
0
1
2
2
4
š§ Practice Questions
Find three solutions of x + 2y = 6
Check whether (3,2) satisfies equation
Draw graph of x ā y = 1
Write equation of horizontal line
š For extra practice, explore platforms like BYJU’S.
š Important Points to Remember
Linear equation has degree 1
Graph is always straight line
Infinite solutions possible
ā Common Mistakes
Wrong substitution
Plotting wrong points
Not drawing straight line
š§ Tips for Students
Practice graphs regularly
Understand concept, not memorize
Solve NCERT questions
š Internal Linking Idea
š Also read: Number System Class 9 Notes
ā Conclusion
Linear Equations in Two Variables is a very important topic. With practice and clear understanding, students can easily solve questions and score high marks.
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