2021 Fall AMC 10A Problems/Problem 14
Contents
Problem
How many ordered pairs of real numbers satisfy the following system of equations?
Solution 1 (Graphing)
The second equation is . We know that the graph of is a very simple diamond shape, so let's see if we can reduce this equation to that form: We now have two separate graphs for this equation and one graph for the first equation, so let's put it on the coordinate plane: We see from the graph that there are intersections, so the answer is .
~KingRavi
Video Solution
~Education, the Study of Everything
Video Solution
https://youtu.be/zq3UPu4nwsE?t=974
Video Solution by WhyMath
~savannahsolver
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.