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Line through the intersection of two lines with a given intercept condition

This type of question, asked 4 times: 3 May 2023 S2, 11 Apr 2026 S1, 15 Apr 2026 S2, 19 May 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    3 May 2023 S2

    101
    The equation of the line passing through the point of intersection of the lines 3x−y=53x-y=5 and x+3y=1x+3y=1 and making equal intercepts on the axes is

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  2. Question 2

    11 Apr 2026 S1

    56
    The equation of a line passing through the point of the intersection of the lines x−y+1=0x - y + 1 = 0 and 2x+3y−8=02x + 3y - 8 = 0 and having x intercept 33 is

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  3. Question 3

    15 Apr 2026 S2

    58
    The equation of the line passing through the point of intersection of the lines x+2y+6=0x + 2y + 6 = 0 and 2x−y=22x - y = 2 and making an intercept 5 on the y-axis is

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  4. Question 4

    19 May 2026 S1

    60
    The equation of the line which passes through the point of intersection of lines x+2y+6=0x + 2y + 6 = 0, 2x−y=22x - y = 2 and which makes intercept 5 on Y - axis is

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