Difference between revisions of "1954 AHSME Problems/Problem 12"

(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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<math>2x-3y=7\implies 4x-6y=14</math>
 
<math>2x-3y=7\implies 4x-6y=14</math>
Then <math>4x-6y=14=20</math>, which is untrue, so there are no solutions; <math>\fbox{C}</math>
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Then <math>4x-6y=14=20</math>, which is false, so there are no solutions; <math>\fbox{C}</math>
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==See Also==
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{{AHSME 50p box|year=1954|num-b=11|num-a=13}}
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{{MAA Notice}}

Latest revision as of 20:42, 17 February 2020

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 false, so there are no solutions; $\fbox{C}$

See Also

1954 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
All AHSME Problems and Solutions


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