This document provides an overview of linear equations in two variables. It begins by introducing the standard form of a linear equation: ax + by + c = 0. It then discusses two methods for solving a pair of linear equations: the graphical and algebraic methods. Examples are provided to demonstrate plotting points from a linear equation in standard form and determining if a given point lies on the line. The document also notes that equations of the form x = n or y = n represent lines parallel to the y-axis or x-axis, respectively.

1. LINEAR EQUATION IN
TWO VARIABLE

2. Let’s start with the journey with some basics here:
(+,+)(-,+)
(-,-) (+,-)
Learning the Cartesian sign is important
.
This is the origin
The Quadrants

3. The word LINEAR originates from:
Today we will study the equation
for lines.
In a Graph, these equations are used
To get the position of a line

4. Linear equation in two variable
THE STANDARD
FORM:
ax+by+c=0
Here, a and b
are the
constants that
cannot be 0
Example:
47x+7y=9c can be zero

5. There are 2 methods to solve
A Pair of Linear equation
1  Graphical method
2  Algebraic method
ax+by+c=0

6. Lets solve some examples quickly:
Q. We need to plot the diagram for 5x+4y+20=0
and check whether (0,-5) lies in it.
STEP 1:
Assume
a value
for x and
find the
value of
y
x
y
We will take three observation to plot the point.
Lets take the points -1,0,1 for x
When x=-1
5(-1)+4y+20=0
.’.-5+4y=-20
.’.4y=-20+5
y=-15/4=-3.75
When x=0
5(0)+4y+20=0
.’.4y=-20
.’.y=-20/4
y=-5
When x=-1
5(1)+4y+20=0
.’.5+4y=-20
.’.4y=-20-5
y=-25/4=-6.25
-1
-3.75
0
-5
1
-6.25

7. x -1 0 1
y -3.75 -5 -6.25
From this observation
We come to know that (0,-5)
Lies on the line
Now lets plot our graph
This is our graph based on
Cartesian sign
Remember to label
The points and the line
(0,-5)
(-1,-3.75)
(1,-6.25)
(0,0)
And we are done!

8. The standard form: ax+bx+c=0
x+y=5 x+y-5=0
3x+7y-66=0
8y-4x=-12  -4x+8y+12=0
2x+
𝟐
𝟑
𝐲 = 𝟕  2x+
𝟐
𝟑
𝐲 − 𝟕 =0
Lets do some quick activity:
Determine the coefficints and the constants from the given expressions
a b c
1 1 -5
3 7 -66
8 -4 12
2 𝟐
𝟑
-7

9. Quick facts:
For the equations like:
x=n, where n can be any
integer.
The line on the graph
will always be
Parallel to y-axis
Examples:
X=-5
X=3 X=6
X=-2
They’re parallel to y-axis
Y-axis
X-axis

10. Quick facts:
For the equations like:
y=n, where n can be any
integer.
The line on the graph
will always be
Parallel to x-axis
Examples:
y=-5
y=3 y=6
y=-2
They’re parallel to x-axis
Y-axis
X-axis

11. THANK YOU