Question

Assertion (A): If the pair of equation
x  2y  7  0, 3x  ky 21 0
represents coincident
lines, then the value of k is 6.
Reason (R) : The pair of linear equations are coincident lines if they have no solution.

Answer 1

Assertion is true but reason is false

Answer 2

Given :

A pair of equation ,

x + 2y + 7 = 0   (i) ; and

3x + ky + 21 = 0    (ii)

To find :

To prove if the lines are coincident and then the value of k is 6.

Explanation :

If we say the given lines are coincident , then they must have at least one point in common.

Lets say the point is (x ,y)

Now,  if we multiply first equation by 3 , it becomes 3x + 6y + 21 = 0

Subtracting this equation with the second equation we get,

                                     (k -6)y   = 0

therefore,                             k  = 6

Hence, the given lines are coincident and therefore the value of k comes 6.

Final Answer :  

The assertion in the question stands true while the reason is false . As , if there are no common points between the lines, they cannot be concluded coincident.

Although your question is incomplete , you might be referring to this question below .

Assertion (A): If the pair of equation x + 2y + 7 =0 and 3x + ky + 21 =0 represent coincident lines ,then the value of k is 6.

Reason (R): The pair of linear equations are coincident lines if they have no solution.