Difference between revisions of "1980 AHSME Problems/Problem 29"
(Created page with "== Problem == How many ordered triples (x,y,z) of integers satisfy the system of equations below? <cmath>\begin{array}{l} x^2-3xy+2yz-z^2=31 \\ -x^2+6yz+2z^2=44 \\ x^2+xy+8z^2...") |
m (→Problem) |
||
| Line 7: | Line 7: | ||
<math>\text{(A)} \ 0 \qquad | <math>\text{(A)} \ 0 \qquad | ||
\text{(B)} \ 1 \qquad | \text{(B)} \ 1 \qquad | ||
| − | \text{(C)} \ 2 \qquad | + | \text{(C)} \ 2 \qquad \\ |
| − | \text{(D)}\ \text{a finite number greater than 2}\qquad | + | \text{(D)}\ \text{a finite number greater than 2}\qquad\\ |
| − | \text{(E)}\ \text{infinitely many} </math> | + | \text{(E)}\ \text{infinitely many} </math> |
| − | |||
== Solution == | == Solution == | ||
Revision as of 01:28, 3 October 2014
Problem
How many ordered triples (x,y,z) of integers satisfy the system of equations below?
![\[\begin{array}{l} x^2-3xy+2yz-z^2=31 \\ -x^2+6yz+2z^2=44 \\ x^2+xy+8z^2=100\\ \end{array}\]](http://latex.artofproblemsolving.com/b/7/7/b774d8b5fdfb7de105678633783fa9df4b81772a.png)
Solution
See also
| 1980 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 28 |
Followed by Problem 30 | |
| 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 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
