This document discusses linear equations in two variables. It begins with definitions, stating that a linear equation in two variables is an equation of the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not both zero. It then provides 8 facts about linear equations, such as that their graphs are straight lines and they have infinitely many solutions. It concludes by outlining procedures for finding a solution, finding a solution from a graph, and drawing the graph of a linear equation.

1. In this document you can review important
• Definitions
• Facts
• Procedures
Class – IX, CBSE
MB0904: Linear Equations in
Two variables
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2. What is a Linear
Equations in two
variables?
Class – IX,CBSE
MB0904: Linear Equations in Two
variables
Important Definitions
Topic: Linear Equations
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3. What is a Linear
Equations in two
variables?
Class – IX,CBSE
Important Definitions
An equation of the form
ax+by+c = 0, where a, b and are
real numbers, such that a and b are not
both zero, is called a linear equation
in two variables.
c
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MB0904: Linear Equations in Two
variables
Topic: Linear Equations

4. Fact # 1
A linear equation in two variables has infinitely many solutions.
Class – IX,CBSE
Important Facts
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MB0904: Linear Equations in Two
variables
Topic: Linear Equations

5. Fact # 2
The graph of every linear equation in two variables is a straight line.
Class – IX,CBSE
Important Facts
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MB0904: Linear Equations in Two
variables
Topic: Linear Equations

6. Fact # 3
is the equation of the y-axis.
Class – IX,CBSE
Important Facts
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MB0904: Linear Equations in Two
variables
0x
Topic: Linear Equations

7. Fact # 4
is the equation of the x-axis.
Class – IX,CBSE
Important Facts
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MB0904: Linear Equations in Two
variables
0y
Topic: Linear Equations

8. Fact # 5
The graph of is a straight line parallel to the y-axis.
Class – IX,CBSE
Important Facts
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MB0904: Linear Equations in Two
variables
x a
Topic: Linear Equations

9. Fact # 6
The graph of is a straight line parallel to the x-axis.
Class – IX,CBSE
Important Facts
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MB0904: Linear Equations in Two
variables
y a
Topic: Linear Equations

10. Fact # 7
An equation of the type represents a line passing through the
origin.
Class – IX,CBSE
Important Facts
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MB0904: Linear Equations in Two
variables
y mx
Topic: Linear Equations

11. Fact # 8
Every point on the graph of a linear equation in two variables is a
solution of the linear equation. Moreover, every solution of the linear
equation is a point on the graph of the linear equation.
Class – IX,CBSE
Important Facts
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MB0904: Linear Equations in Two
variables
Topic: Linear Equations

12. How to find a solution of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
Topic: Solution of a Linear Equation

13. How to find a solution of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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: Assume any value of one of the two variables.Step 1
MB0904: Linear Equations in Two
variables
Topic: Solution of a Linear Equation

14. How to find a solution of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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: Put this value in the equation to get a linear equation in one variable.Step 2
MB0904: Linear Equations in Two
variables
: Assume any value of one of the two variables.Step 1
Topic: Solution of a Linear Equation

15. How to find a solution of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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: Solve the equation obtained in step 2 to find the value of the second variable.Step 3
MB0904: Linear Equations in Two
variables
: Assume any value of one of the two variables.Step 1
: Put this value in the equation to get a linear equation in one variable.Step 2
Topic: Solution of a Linear Equation

16. How to find a solution of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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: The two values (from Step 1 and Step 4) are a solution of the linear equation.Step 4
MB0904: Linear Equations in Two
variables
: Solve the equation obtained in step 2 to find the value of the second variable.Step 3
: Assume any value of one of the two variables.Step 1
: Put this value in the equation to get a linear equation in one variable.Step 2
Topic: Solution of a Linear Equation

17. How to find a solution of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
: The two values (from Step 1 and Step 4) are a solution of the linear equation.Step 4
: Solve the equation obtained in step 2 to find the value of the second variable.Step 3
: Assume any value of one of the two variables.Step 1
: Put this value in the equation to get a linear equation in one variable.Step 2
: Note that we always write the -value first when writing the solution as a pair.xStep 5
Topic: Solution of a Linear Equation

18. How to find a solution from the graph of a linear equation in
2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
Topic: Solution of a Linear Equation

19. How to find a solution from the graph of a linear equation in
2 variables?
Class – IX,CBSE
Important Procedures
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:Select any point on the line in the graph.Step1
MB0904: Linear Equations in Two
variables
Topic: Solution of a Linear Equation

20. How to find a solution from the graph of a linear equation in
2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
:Select any point on the line in the graph.Step1
:Draw a vertical line from the point to intersect the -axis.xStep2
Topic: Solution of a Linear Equation

21. How to finding a solution from the graph of a linear
equation in 2 variables?
Class – IX,CBSE
Important Procedures
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How to find a solution from the graph of a linear equation in
2 variables?
:Select any point on the line in the graph.Step1
:Draw a vertical line from the point to intersect the -axis.xStep2
:Note the point where it intersects the -axis.xStep3
MB0904: Linear Equations in Two
variables
Topic: Solution of a Linear Equation

22. How to finding a solution from the graph of a linear
equation in 2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
How to find a solution from the graph of a linear equation in
2 variables?
:Select any point on the line in the graph.Step1
:Draw a vertical line from the point to intersect the -axis.xStep2
:Note the point where it intersects the -axis.xStep3
:Draw a horizontal line from the point to intersect the -axis.yStep4
Topic: Solution of a Linear Equation

23. How to finding a solution from the graph of a linear
equation in 2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
How to find a solution from the graph of a linear equation in
2 variables?
:Select any point on the line in the graph.Step1
:Draw a vertical line from the point to intersect the -axis.xStep2
:Note the point where it intersects the -axis.xStep3
:Draw a horizontal line from the point to intersect the -axis.yStep4
:Note the point where it intersects the -axis.yStep5
Topic: Solution of a Linear Equation

24. How to finding a solution from the graph of a linear
equation in 2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
How to find a solution from the graph of a linear equation in
2 variables?
:Select any point on the line in the graph.Step1
:Draw a vertical line from the point to intersect the -axis.xStep2
:Note the point where it intersects the -axis.xStep3
:Draw a horizontal line from the point to intersect the -axis.yStep4
:Note the point where it intersects the -axis.yStep5
:A solution of the equation is , .Here is obtained in step 3 and in step 5.x y x yStep6
Topic: Solution of a Linear Equation

25. How to draw the graph of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
Topic: Graph of a Linear Equation

26. How to draw the graph of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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:Write the equation in standard form 0 .ax by cStep1
MB0904: Linear Equations in Two
variables
Topic: Graph of a Linear Equation

27. How to draw the graph of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
Learn Math for Free. Visit www.ganitgurooz.com
MB0904: Linear Equations in Two
variables
:Write the equation in standard form 0 .ax by cStep1
:Put 0 to get by 0.x cStep2
Topic: Graph of a Linear Equation

28. How to draw the graph of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
How to draw the graph of a linear equation in 2 variables?
:Write the equation in standard form 0 .ax by cStep1
:Put 0 to get by 0.x cStep2
:Solve this equation to get .
c
y
b
Step3
Topic: Graph of a Linear Equation

29. How to draw the graph of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
Learn Math for Free. Visit www.ganitgurooz.com
MB0904: Linear Equations in Two
variables
:Write the equation in standard form 0 .ax by cStep1
:Put 0 to get by 0.x cStep2
:Solve this equation to get .
c
y
b
Step3
:Now put 0 in the equation in step 1 to get 0.y ax cStep4
Topic: Graph of a Linear Equation

30. How to draw the graph of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
:Write the equation in standard form 0 .ax by cStep1
:Put 0 to get by 0.x cStep2
:Solve this equation to get .
c
y
b
Step3
:Now put 0 in the equation in step 1 to get 0.y ax cStep4
:Solve this equation to get .
c
x
a
Step5
Topic: Graph of a Linear Equation

31. How to draw the graph of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
Learn Math for Free. Visit www.ganitgurooz.com
MB0904: Linear Equations in Two
variables
:Write the equation in standard form 0 .ax by cStep1
:Put 0 to get by 0.x cStep2
:Solve this equation to get .
c
y
b
Step3
:Now put 0 in the equation in step 1 to get 0.y ax cStep4
:Solve this equation to get .
c
x
a
Step5
:You have two solutions 0, and ,0 .
c c
b a
Step6
Topic: Graph of a Linear Equation

32. How to draw the graph of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
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MB0904: Linear Equations in Two
variables
:Join these points to obtain a line.Step8
How to draw the graph of a linear equation in 2 variables?
:Locate and plot the points 0, and ,0 n a coordinate plane (on a graph paper).
c c
b a
Step7
Topic: Graph of a Linear Equation

33. How to draw the graph of a linear equation in 2 variables?
Class – IX,CBSE
Important Procedures
Learn Math for Free. Visit www.ganitgurooz.com
MB0904: Linear Equations in Two
variables
:Join these points to obtain a line.Step8
How to draw the graph of a linear equation in 2 variables?
:Locate and plot the points 0, and ,0 n a coordinate plane (on a graph paper).
c c
b a
Step7
:Join these points to obtain a line.Step8
Topic: Graph of a Linear Equation