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Solve a pair of linear equations (intersection point) and use the solution

This type of question, asked 4 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 8 Aug 2022 Tier II. All 4 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    97
    The graphs of the equations 3x−20y−2=03x - 20y - 2 = 0 and 11x−5y+61=011x - 5y + 61 = 0 intersect at P(a,b). What is the value of (a2+b2−ab)/(a2−b2+ab)(a^2 + b^2 - ab)/(a^2 - b^2 + ab)?

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  2. Question 2

    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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  3. Question 3

    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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  4. Question 4

    8 Aug 2022 Tier II

    77
    What is the solution of the following equations ? 2x+3y=122x + 3y = 12 and 3x−2y=53x - 2y = 5

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