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Pair of linear equations: classify, or find k for unique, no or infinitely many solutions

This type of question, asked 3 times: CDS 1 2017, CDS 2 2021, CDS 1 2026. All 4 questions below, oldest first.

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  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 1 2017

    47
    The system of equations 2x+4y=62x + 4y = 6 and 4x+8y=84x + 8y = 8 is

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  3. Question 3

    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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  4. Question 4

    CDS 1 2026

    10
    For what integral value of k, the system of equations kx−5y+6=0kx - 5y + 6 = 0 and 4(k−1)y−12x+3=04(k - 1)y - 12x + 3 = 0 has no solution ?

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