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2006 AMC 10BProblem 12P11-15~2 minPrint
Coordinate GeometryLinear Equations & Word ProblemsSet up the equation/formula and compute; no special trick neededTest small/specific values or special cases to find or verify the answer

The lines x=14y+ax=\frac{1}{4}y+a and y=14x+by=\frac{1}{4}x+b intersect at the point (1,2)(1,2) . What is a+ba+b ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.