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LINEAR EQUATION IN
TWO VARIABLE
Let’s start with the journey with some basics here:
(+,+)(-,+)
(-,-) (+,-)
Learning the Cartesian sign is important
.
This is the origin
The Quadrants
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
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
There are 2 methods to solve
A Pair of Linear equation
1  Graphical method
2  Algebraic method
ax+by+c=0
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
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!
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
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
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
THANK YOU

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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