Difference between revisions of "1950 AHSME Problems/Problem 14"
(Created page with "== Problem== For the simultaneous equations <cmath>2x-3y=8\\6y-4x=9</cmath> <math> \textbf{(A)}\ x=4,y=0\qquad\textbf{(B)}\ x=0,y=\frac{3}{2}\qquad\textbf{(C)}\ x=0,y=0\qquad\\...") |
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== Problem== | == Problem== | ||
| − | For the simultaneous equations <cmath>2x-3y=8 | + | For the simultaneous equations <cmath>2x-3y=8</cmath> |
| + | <cmath>6y-4x=9</cmath> | ||
<math> \textbf{(A)}\ x=4,y=0\qquad\textbf{(B)}\ x=0,y=\frac{3}{2}\qquad\textbf{(C)}\ x=0,y=0\qquad\\ \textbf{(D)}\ \text{There is no solution}\qquad\textbf{(E)}\ \text{There are an infinite number of solutions} </math> | <math> \textbf{(A)}\ x=4,y=0\qquad\textbf{(B)}\ x=0,y=\frac{3}{2}\qquad\textbf{(C)}\ x=0,y=0\qquad\\ \textbf{(D)}\ \text{There is no solution}\qquad\textbf{(E)}\ \text{There are an infinite number of solutions} </math> | ||
| Line 17: | Line 18: | ||
Something is clearly contradictory so <math>\boxed{\mathrm{(D)}\text{ There is no solution}.}</math> | Something is clearly contradictory so <math>\boxed{\mathrm{(D)}\text{ There is no solution}.}</math> | ||
| + | |||
| + | Alternatively, note that the second equation is a multiple of the first except that the constants don't match up. So, there is no solution. | ||
==See Also== | ==See Also== | ||
| − | {{AHSME box|year=1950|num-b=13|num-a=15}} | + | {{AHSME 50p box|year=1950|num-b=13|num-a=15}} |
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 17:15, 21 December 2015
Problem
For the simultaneous equations ![\[2x-3y=8\]](http://latex.artofproblemsolving.com/6/3/d/63dbf1b5178e1e8b786f72f6a4c29361eadacf11.png)
![\[6y-4x=9\]](http://latex.artofproblemsolving.com/d/e/e/dee63f1ea5313977e00e03b65b1d3ce89a70ccc0.png)
Solution
Try to solve this system of equations using the elimination method.
Something is clearly contradictory so 
Alternatively, note that the second equation is a multiple of the first except that the constants don't match up. So, there is no solution.
See Also
| 1950 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
