MathemaMathematics Paper tics Paper PresentatiPresentati

ononConditions For Conditions For Consistency for a Consistency for a

Given Pair Of Given Pair Of Linear EquationLinear Equation

What does Linear Equation in Two Variable Consists Of?

ax+by+c=0 Where ‘x’ & ‘y’ are the Variables (Whose Values We Don’t Know)

& ‘a’, ‘b’ & ‘c’ are Constants (Any Real Number where a ≠ 0 & b ≠ 0)

2x+4y+3=0

a=2 b=4 c=3

Unique Solution

Unique Solution Intersecting Lines

Unique Solution2x-y-5=0 --------(i)x-y-3=0 --------(ii)

= =

y

X' x

0

y’

Table Of Roots For Eqn (i)

x 3 2

y 1 -1

Table Of Roots For Eqn (ii)

x 3 4

y 0 1

A (3,1)

B (2,-1)

C (3,0)

D (4,1)

1

2

Scale: 1box = 1unitScale: 1box = 1unitScale: 1box = 1unitScale: 1box = 1unit

2x-

y-5

=0

2x-

y-5

=0

x-y-

3=0

x-y-

3=0

Many Solution Many Solutions Coincident Line

Many Solutionx+y-5=0 ----------(i)2x+2y-10=0 -----------(ii)

= = =

y

1

X' 0 x

2

y’

Table Of Roots For Eqn (i)

x 0 5

y 5 0

Table Of Roots For Eqn (ii)

x 1 2

y 4 3

A (0,5)

B (5,0)

C (1,4) D (2,3)

Scale: 1box = 1unitScale: 1box = 1unitScale: 1box = 1unitScale: 1box = 1unit

x+y-5=

0

x+y-5=

0

2x+2y-10=

0

2x+2y-10=

0

No SolutionNo Solution Parallel Lines

No Solution2x+y-160=0 ---------(i)2x+y-150=0 ---------(ii)

= = =

y 1

X' 0 2 x

y’

Table Of Roots For Eqn (ii)

x 50 30

y 50 90

Scale: 1box = 10unitScale: 1box = 10unitScale: 1box = 10unitScale: 1box = 10unit Table Of Roots For Eqn (i)

x 50 40

y 60 80A (50,60)

B (40,80)

C (50,50)

D (30,90)

2x+

y-150=

0

2x+

y-150=

0

2x+

y-160=

0

2x+

y-160=

0

Unique Solution Many Solution No Solution

Consistent Consistent Inconsistent

IntersectingLines

CoincidentLines

ParallelLines

Thank You