MathDB
1987 AMC 12 #11 - Simultaneous Equations

Source:

December 31, 2011
AMC

Problem Statement

Let cc be a constant. The simultaneous equations \begin{align*} x-y = &\ 2 \\ cx+y = &\ 3 \\ \end{align*} have a solution (x,y)(x, y) inside Quadrant I if and only if
<spanclass=latexbold>(A)</span> c=1<spanclass=latexbold>(B)</span> c>1<spanclass=latexbold>(C)</span> c<32<spanclass=latexbold>(D)</span> 0<c<32<spanclass=latexbold>(E)</span> 1<c<32 <span class='latex-bold'>(A)</span>\ c=-1 \qquad<span class='latex-bold'>(B)</span>\ c>-1 \qquad<span class='latex-bold'>(C)</span>\ c<\frac{3}{2} \qquad<span class='latex-bold'>(D)</span>\ 0<c<\frac{3}{2}\\ \qquad<span class='latex-bold'>(E)</span>\ -1<c<\frac{3}{2}