5. • LINEAR EQUATION
• FORM OF LINEAR EQUATION
• TYPES OF LINEAR EQUATION
• GRAPH OF A EQUATION
• TYPES OF GRAPH
• HOW CAN KNOW ABOUT GRAPH?
• EXAMPLES OF TYPES OF GRAPH
• FORMULA OF CROSS – MULTIPLICATION
• SOLVE QUESTION
6. LINEAR EQUATION
Linear equations are functions which have
two variables. They have an independent
and dependent variable.
Independent Variables Dependent Variables
Independent variables Dependent variables
are variables that you are variables that you
put into the equations solve for
7. The general form for a pair of linear
equation in two variables of x and y is ->
a1 + b1 +c1 = 0
a2 + b2 + c2 = 0
Where a1,b1,c1,a2,b2,c2 are real numbers and
a, and b both are not zero.
8. What is linear equation in two variable?
Equations of the form ax + by = c are called linear
equations in two variables.
How many types of method to find the
solution of pair of linear equation?
There are of four types
1. Elimination method
2. Substitution method
3. Cross-multiplication method
4. Graph method
9. Linear equation graph
y
This is the graph of the
equation 2x + 3y = 12.
x
-2 2
The point (0,4) is the y-intercept.
The point (6,0) is the x-intercept.
10. The graph of a pair of variable is
represnted by two lines
• If the line intersect at a point, then
that point gives a unique solution
and the pair of equation is
consistent.
• If the line is coincide, then there
are infinite many solution and the
pair of equation is consistent
• If the line are parallel, then there
are no solution and the pair of
equation is inconsistent.
11. a1 ≠ b1 so the pair of linear equation is unique.
a2 b2
a1=b1 ≠c1 so the pair of linear equation is no
a2 b2 c2 solution.
a1=b1= c1 so the pair of linear equation is infinity
a2 b2 c2 many solution
12. Two lines are parallel if
If a1=b1 ≠c1 so the lines will be parallel.
a2 b2 c2
(0, 4)
Example:
The lines 2x – y = 3
and 2x –y = -4
2 = -1 ≠ 3
2 -1 -4
(0, -3)
The lines are parallel.
13. Two lines are coincident if
If a1=b1 =c1 so the lines will be coincident.
a2 b2 c2
Example:
.
The lines 9x + 3y = -12 (-2,2)
and18x + 6y = -24
9 = 3 ≠ -12 (-1,-1)
18 6 -24
0,-4)
The lines are coincident.
14. Two lines are intersect if
If a1=b1 =c1 so the lines will be intersect.
a2 b2 c2
(0,5)
Example:
The lines 2x + y = 5 (2,1)
and 2x –2y = 2 (0,1)
2≠1
2 -2
The lines are Intersect.
15. How to solve equation by cross
multiplication method?
Method to solve equation by cross
multiplication in linear equation in two
variable.
x = b1c2 – c1b2 y = c1a2 – a1c2
a1b2 – b1a2 a1b2 – b1a2
