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2013 AMC 10B Problem 14

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2013 AMC 10B Problem 14AMC 10 Step by Step
Name:                             Date: September 13, 2026
Algebraic Manipulation · difficulty 2 of 5 · about 3 min · position P11-15

Define a♣b=a2b−ab2a\clubsuit b=a^2b-ab^2 . Which of the following describes the set of points (x,y)(x, y) for which x♣y=y♣xx\clubsuit y=y\clubsuit x ?

  1. A)

    a finite set of points\text{a finite set of points}

  2. B)

    one line\text{one line}

  3. C)

    two parallel lines\text{two parallel lines}

  4. D)

    two intersecting lines\text{two intersecting lines}

  5. E)

    three lines\text{three lines}

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