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2014 AMC 10A Problems/Problem 21

Revision as of 21:54, 6 February 2014 by TheMaskedMagician (talk | contribs) (Created page with "==Problem== Positive integers <math>a</math> and <math>b</math> are such that the graphs of <math>y=ax+5</math> and <math>y=3x+b</math> intersect the <math>x</math>-axis at the s...")
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Problem

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

$\textbf{(A)}\ {-20}\qquad\textbf{(B)}\ {-18}\qquad\textbf{(C)}\ {-15}\qquad\textbf{(D)}\ {-12}\qquad\textbf{(E)}\ {-8}$

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