2021 Fall AMC 10A Problems/Problem 14
Problem
How many ordered pairs of real numbers satisfy the following system of equations?
Solution (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:
import graph; [asy]
Label f; f.p=fontsize(6); xaxis(-8,8,Ticks(f, 2.0,0.5)); yaxis(-8,8,Ticks(f, 2.0,0.5))
real f(real x) { return |x| + |y| = 3; } draw(graph(f,-2,2));
real f(real x) { return |x| + |y| = 5; } draw(graph(f,-2,2));
real f(real x) { return x^2+3y = 9; } draw(graph(f,-2,2));
[/asy]
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 |
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