MATHEMATICSPRESENTATION

PRESENTED BY :

RAKSHITA ASATI

10th “B”

1020 “B”

Data Collection1. For unique solution a1/a2 = b1/b2 Lines intersect at a

point

x+3y = 0 2x-3y = 0

EQUATION

ANALYSIS

0

0 62 0

xy

For eq.x+3y=6

ANALYSIS

For eq. 2x-3y = 0

xy -

2

3-40

GRAPH

xx

y

y

-1

1-2

32 4

-4

-1

-3

(0,2)

(6,0)

(0,-4)

5

1

X+3y=0

2x+3y=6

Data Collection

2. For no solution a1/a2 = b1/b2 =

c1/c2 Lines are

parallel

x+2y-4 = 02x+4y-12=0

EQUATION

ANALYSISFor eq. x+2y-4 = 0

xy 2 0

40

For eq.2x+4y-12=0

x

y 3

0 6

0

GRAPH y

(0,3)

y

(4,0) (6,0)(0,2)

x x

3

1

1 2

5

3

-1

-1

4

4

2

65

2x+4y-12=0x+2y-4=0

Data Collection For infinitely many solution a1/a2 =

b1/b2 = c1=c2 Lines

are coincident

EQUATION 2x+3y = 9 4x+6y = 18

AnalysisFor eq. 2x+3y = 9

xy

4.503 0

For eq. 4x+6y = 18

0XY 3

31

Graph

-1 1

12

3 4

-1

2

54

5xx

y

y

(0,3)(3,1)

(4.5,0)

4x+6y=18

2x+3y=9

THANXXXX

!!!!!!!!