Difference between revisions of "1987 AHSME Problems/Problem 11"

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Let <math>c</math> be a constant. The simultaneous equations
 
Let <math>c</math> be a constant. The simultaneous equations
<cmath>\begin{align*}x-y = &\ 2 \\cx+y = &\ 3 \\\end{align}</cmath>
+
<cmath>\begin{align*}x-y = &\ 2 \\cx+y = &\ 3 \\\end{align*}</cmath>
 
have a solution <math>(x, y)</math> inside Quadrant I if and only if
 
have a solution <math>(x, y)</math> inside Quadrant I if and only if
  

Revision as of 13:10, 1 March 2018

Problem

Let $c$ be a constant. The simultaneous equations \begin{align*}x-y = &\ 2 \\cx+y = &\ 3 \\\end{align*} have a solution $(x, y)$ inside Quadrant I if and only if

$\textbf{(A)}\ c=-1 \qquad \textbf{(B)}\ c>-1 \qquad \textbf{(C)}\ c<\frac{3}{2} \qquad \textbf{(D)}\ 0<c<\frac{3}{2}\\ \qquad \textbf{(E)}\ -1<c<\frac{3}{2}$

See also

1987 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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All AHSME Problems and Solutions

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