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Source: 1964 AHSME Problem 18

August 23, 2013
AMC

Problem Statement

Let nn be the number of pairs of values of bb and cc such that 3x+by+c=03x+by+c=0 and cx−2y+12=0cx-2y+12=0 have the same graph. Then nn is:
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> finite but more than 2<spanclass=′latex−bold′>(E)</span> greater than any finite number <span class='latex-bold'>(A)</span>\ 0\qquad<span class='latex-bold'>(B)</span>\ 1\qquad<span class='latex-bold'>(C)</span>\ 2\qquad<span class='latex-bold'>(D)</span>\ \text{finite but more than 2}\qquad<span class='latex-bold'>(E)</span>\ \text{greater than any finite number}
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