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System with Equation, Inequality

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January 11, 2009
inequalitiesanalytic geometrygraphing linesslopealgebralinear equation

Problem Statement

Let n n be the number of number-pairs (x,y) (x,y) which satisfy 5y \minus{} 3x \equal{} 15 and x^2 \plus{} y^2 \le 16. Then n n is: <spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> more than two, but finite<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{more than two, but finite} \qquad <span class='latex-bold'>(E)</span>\ \text{greater than any finite number}
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