Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1954 AHSME Problems/Problem 12

Revision as of 12:59, 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)}\ ...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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; $\fbox{C}$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1954_AHSME_Problems/Problem_12&oldid=78797"