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Simultaneous Linear Equations

If a pair of ...

Question

If a pair of lines are coincident, then find the number of solutions.

A

A unique solution

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B

Infinitely many solutions

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C

No Solution

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D

None of the above

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Solution

The correct option is B Infinitely many solutions
If a pair of lines are coincident, then both the lines are exactly the same when plotted in the cartesian plane.
Hence, there will be infinitely many solutions.

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Q. Assertion :If the pair of lines are coincident, then we say that pair is consistent and it has a unique solution. Reason: If the pair of lines are parallel, then the pair has no solution and is called inconsistent pair of equations.

Q. STATEMENT - 1 : If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is consistent.
STATEMENT - 2 : If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is inconsistent.

Q. If a pair of linear equations is consistent with a unique solution, then the lines representing them are _______.

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Q. Coincident lines have infinite solutions. Which among the following pairs of lines are coincident?

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