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1954 AHSME Problems/Problem 12

Revision as of 11:59, 6 June 2016 by Katzrockso (talk | contribs) (Created page with "== Problem 12== The solution of the equations <cmath>\begin{align*}2x-3y &=7 \\ 4x-6y &=20\end{align*}</cmath> is: <math>\textbf{(A)}\ x=18, y=12 \qquad \textbf{(B)}\ ...")
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Problem 12

The solution of the equations

\begin{align*}2x-3y &=7 \\ 4x-6y &=20\end{align*}

is:

$\textbf{(A)}\ x=18, y=12 \qquad \textbf{(B)}\ x=0, y=0 \qquad \textbf{(C)}\ \text{There is no solution} \\ \textbf{(D)}\ \text{There are an unlimited number of solutions}\qquad \textbf{(E)}\ x=8, y=5$

Solution

$2x-3y=7\implies 4x-6y=14$ Then $4x-6y=14=20$, which is untrue, so there are no solutions; $\fbox{C}$

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