Difference between revisions of "1980 AHSME Problems/Problem 29"
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How many ordered triples (x,y,z) of integers satisfy the system of equations below? | How many ordered triples (x,y,z) of integers satisfy the system of equations below? | ||
| − | <cmath>\begin{array}{l} x^2-3xy+ | + | <cmath>\begin{array}{l} x^2-3xy+2y^2-z^2=31 \\ -x^2+6yz+2z^2=44 \\ x^2+xy+8z^2=100\\ \end{array} </cmath> |
<math>\text{(A)} \ 0 \qquad | <math>\text{(A)} \ 0 \qquad | ||
Revision as of 18:31, 6 January 2019
Problem
How many ordered triples (x,y,z) of integers satisfy the system of equations below?
![\[\begin{array}{l} x^2-3xy+2y^2-z^2=31 \\ -x^2+6yz+2z^2=44 \\ x^2+xy+8z^2=100\\ \end{array}\]](http://latex.artofproblemsolving.com/8/7/5/875243b329d45c8a54367576d9f82e8999df15c7.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. 
