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2014 AMC 10A Problem 21

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2014 AMC 10A Problem 21AMC 10 Step by Step
Name:                             Date: September 13, 2026
Diophantine Equations · difficulty 3 of 5 · about 3 min · position P21-25

Positive integers aa and bb are such that the graphs of y=ax+5y=ax+5 and y=3x+by=3x+b intersect the xx -axis at the same point. What is the sum of all possible xx -coordinates of these points of intersection?

  1. A)

    −20{-20}

  2. B)

    −18{-18}

  3. C)

    −15{-15}

  4. D)

    −12{-12}

  5. E)

    −8{-8}

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