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Two lines intersect at P: which other given line also passes through P

The same question, asked 2 times: 29 Jan 2022 Tier II*, 3 Feb 2022 Tier II. Every wording below, oldest first.

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  1. Question 1

    29 Jan 2022 Tier II

    44
    The graphs of the equations 4x+13y=834x + \frac{1}{3}y = \frac{8}{3} and 12x+34y+52=0\frac{1}{2}x + \frac{3}{4}y + \frac{5}{2} = 0 intersect at a point P. The point P also lies on the graph of the equation:

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  2. Question 2

    3 Feb 2022 Tier II

    49
    The graphs of the equations 7x+11y=37x + 11y = 3 and 8x+y=158x + y = 15 intersect at the point P, which also lies on the graph of the equation:

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