31264422
Description
Mind Map by JUDHAJEET GHOSH, updated more than 1 year ago
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Created by JUDHAJEET GHOSH
almost 3 years ago
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Pair of Linear Equations in
Two Variables
- Geometric [Graphical] Solution
- Single and Unique
Solution
- Intersecting lines
- Consistent
- If the Pair of Linear Equations are
ax+by+c= 0 and Ax+By+C=0 then
a/A ≠ b/B ≠ c/C
- Consistent
- Intersecting lines
- No solutions at all
- Parallel Lines
- Inconsistent
- If the Pair of Linear
Equations are ax+by+c=
0 and Ax+By+C=0 then
a/A = b/B ≠ c/C
- Inconsistent
- Parallel Lines
- Infinitely Many Solutions
- Identical or Overlapping Lines
- Consistent
- If the Pair of Linear
Equations are
ax+by+c= 0 and
Ax+By+C=0 then
a/A = b/B = c/C
- Consistent
- Identical or Overlapping Lines
- Single and Unique
Solution
- Algebraic Solution
- Substitution Method
- We Substitute the Value of one
Variable by Expressing it in the Term
of the Other Variable to Solve the
Pair of Linear equations
- We Substitute the Value of one
Variable by Expressing it in the Term
of the Other Variable to Solve the
Pair of Linear equations
- Elimination Method
- We Eliminate
one Variable
First to Get a
Linear
Equation in
one Variable
and Then
Solving it we
Find the other
Variable
- We Eliminate
one Variable
First to Get a
Linear
Equation in
one Variable
and Then
Solving it we
Find the other
Variable
- Cross
Multiplication
Method
- If the Pair of Linear
Equations are
ax+by+c= 0 and
Ax+By+C=0 then
x/(b*-B*c)=
y/(c*A-C*a)=
1/(a*B-A*b)
- If the Pair of Linear
Equations are
ax+by+c= 0 and
Ax+By+C=0 then
x/(b*-B*c)=
y/(c*A-C*a)=
1/(a*B-A*b)
- Substitution Method
- Equations Reducible to a
Pair of Linear Equations
- in Pair of Equations
with Variables in
the Denominator
we change the
Fraction To Another
Variable
- Eg. Let the Pair of Equations be
2/x+3/y= 13 and 5/x-4/y= -2
- We take (1/x) as 'p' and
(1/y) as 'q'
- Then the Equations are
2p+3q=13 and 5p-4q=-2
- After solving for 'p' and 'q' we solve for (1/x)=p and (1/y)=q
- After solving for 'p' and 'q' we solve for (1/x)=p and (1/y)=q
- Then the Equations are
2p+3q=13 and 5p-4q=-2
- We take (1/x) as 'p' and
(1/y) as 'q'
- Eg. Let the Pair of Equations be
2/x+3/y= 13 and 5/x-4/y= -2
- in Pair of Equations
with Variables in
the Denominator
we change the
Fraction To Another
Variable
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