If a pair of linear equations have no solution, then they are

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Consistent

Inconsistent

have infinite solutions

None

answer is B.

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Detailed Solution

Given that a pair of linear equations have no solution.
When any two of linear equations consists of the same variables, then it is called a pair of linear equations.
For example,

a 1 x + b 1 y + c 1 = 0

and

a 2

x + b 2 y + c 2 = 0

.
Any pair of linear equations has no solution, if and only if

a 1 a 2 = b 1 b 2 ≠ c 1 c 2

.
Let us consider the equations

2 x − 3 y = 8

and

4 x − 6 y = 9

.
Substitute the values into

a 1 a 2, b 1 b 2

and

c 1 c 2,

a 1 a 2 = 24, b 1 b 2 = − 3 − 6

and

c 1 c 2 = 89

.
Therefore,

a 1 a 2 = b 1 b 2 ≠ c 1 c 2

, which means the considered pair of equations have no solution.
As a result, the pair of linear equations is said to as inconsistent.
The correct option is (2).

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