Difference between revisions of "2021 Fall AMC 10A Problems/Problem 14"
| Line 1: | Line 1: | ||
| + | ==Problem== | ||
| + | How many ordered pairs <math>(x,y)</math> of real numbers satisfy the following system of equations? | ||
| + | <cmath>x^2+3y=9</cmath> | ||
| + | <cmath>(|x|+|y|-4)^2 = 1</cmath> | ||
| + | <math>\textbf{(A )} 1 \qquad\textbf{(B) } 2 \qquad\textbf{(C) } 3 \qquad\textbf{(D) } 5 \qquad\textbf{(E) } 7</math> | ||
| + | |||
| + | ==Solution== | ||
Revision as of 19:14, 23 November 2021
Problem
How many ordered pairs 
of real numbers satisfy the following system of equations?
![\[x^2+3y=9\]](http://latex.artofproblemsolving.com/c/0/9/c09aed7a84906eb65f1fa163a7a7d92168877583.png)
![\[(|x|+|y|-4)^2 = 1\]](http://latex.artofproblemsolving.com/4/d/d/4dd5d2dee801931df0406925786a98be62e43cc2.png)
Solution
See Also
| 2021 Fall AMC 10A (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 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
