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