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Linear Equations in Two Variables
MADE BY : SHASHI PRKASH
Xth –C
35Line
ar E
quat
ions
Equations of the form ax + by = c are called linear equations in two variables.Where A, B, and C are real numbers and A and B are not both zero.
The point (0,4) is the y-intercept.
The point (6,0) is the x-intercept.
x
y
2-2
This is the graph of the equation 2x + 3y = 12.
(0,4)
(6,0)
The graph of any linear equation in two variables is a straight line
INTERSECTING LINE
Equations of the form are called INTERSECTING LINES
These type of equations have Exactly one solution(unique)
These are consistent lines
Example: x-2y=03x+4y=20
= =
COINCIDENT LINES
Equations of the form are called COINCIDENT LINES
These type of equations have Infinity many no. of solution.
These are consistent lines
Example: 2x+3y=94x+6y=18
= =
=
PARALLEL LINES
Equations of the form are called PARALLEL LINES
These type of equations have no solution.
These are inconsistent lines
Example: x+2y=42x+4y=12
= = =
EXAMPLE :X + y=10X - y=4
x 5 6 7
y 5 4 3
x 3 2 5
y -1 -2 1
Graph
Example: x + y=5
2x+2y=10
x 0 2 1
y 5 3 4
Graph
Example: 2x + y=160
2x+y=150x 60 70 50
y 40 20 60
x 60 50 40
y 30 50 70
Graph
Substitution MethodEXAMPLE : x + y=14
x – y=14
Solution : x + y=14-------------------------1
x – y=14-------------------------2
From equation 1
x =14-y
Put the value of x in equation 2
14-y-y=414-2y=4
14-4=2y10=2y
Y=5
x =14-5X=9
Elimination MethodEXAMPLE : x + y=25
x + 2y=40
x + y=25-------------------------1
x + 2y=40-------------------------2
Solution :
Subtract equation 2 from 1
x + 2y=40- - -
x + y=25
-y=-15
-y=-15Y=15
x + 15=25X=25-15
X=10
Cross-Multiplication
MethodThe general form of cross- multiplication method is:
𝒙𝒃𝟏𝒄𝟐−𝒃𝟐𝒄𝟏
=𝒚
𝒄𝟏𝒂𝟐−𝒄𝟐𝒂𝟏=
𝟏𝒂𝟏𝒃𝟐−𝒂𝟐𝒃𝟏
THANK YOU