Mathematics Paper Presentation Class X
Transcript of Mathematics Paper Presentation Class X
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