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Pair of linear equations with k: condition on k for a unique solution (lines intersect)

The same question, asked 2 times: CDS 1 2017*, CDS 2 2021. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2017

    20
    The pair of linear equations kx+3y+1=0kx + 3y + 1 = 0 and 2x+y+3=02x + y + 3 = 0 intersect each other, if

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  2. Question 2

    CDS 2 2021

    36
    If the system of equations 7x+ky=277x+ky=27 and kx+7y=19kx+7y=19 have unique solution, then which one of the following is correct ?

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