e)For pair of linear equations in two variables write the conditions for unique, infinitely many and
no solution
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Answered by
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Step-by-step explanation:
If then the pair of linear equations has exactly one solution.
If then the pair of linear equations has infinitely many solutions.
If then the pair of linear equations has no solution.
S. No.
Pair of lines
a1/a2
b1/b2
c1/c2
Compare the ratios
Graphical representation
Algebraic interpretation
1
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
a1/a2
b1/ b2
c1/c2
a1 / a2 ≠ b1 / b2
Intersecting lines
Unique solution (Exactly one solution)
2
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
a1/ 2
b1/b2
c1/c2
a1/ a2 = b1 / b2 = c1 / c2
Coincident lines
Infinitely many solutions
3
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
a1/a2
b1/ b2
c1 / c2
a1 / a2= b1 / b2 ≠ c1 / c2
Parallel lines
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