Difference between revisions of "1970 AHSME Problems/Problem 26"
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label("<math>3x + 2y - 12 = 0</math>", (5,-3/2), E, blue); | label("<math>3x + 2y - 12 = 0</math>", (5,-3/2), E, blue); | ||
[/asy] | [/asy] | ||
| + | |||
| + | https://latex.artofproblemsolving.com/c/w/o/cwocgeak.png?time=1513823210175 | ||
Every line passes through the point <math>(2,3)</math>, so the intersection of the two graphs consists of exactly <math>\boxed{1}</math> point. The answer is (B). | Every line passes through the point <math>(2,3)</math>, so the intersection of the two graphs consists of exactly <math>\boxed{1}</math> point. The answer is (B). | ||
Revision as of 21:27, 20 December 2017
Problem
The number of distinct points in the 
-plane common to the graphs of 
and 
is
Solution
The graph of 
is the union of the lines 
and 
(shown in red below). The graph of 
is the union of the lines 
and 
(shown in blue below).
[asy] unitsize(0.8 cm);
draw((-1,0)--(5,0)); draw((0,-1)--(0,5));
draw((0,5)--(5,0),linewidth(1)+red); draw((-1,1)--(5,5),linewidth(1)+red); draw((-1,0)--(4,5),linewidth(1)+blue); draw((2/3,5)--(5,-3/2),linewidth(1)+blue);
label("
", (5,0), NE);
label("
", (0,5), NE);
dot("
", (2,3), E);
label("", (5,0), E, red);
label("", (5,5), E, red);
label("", (4,5), N, blue);
label("
", (5,-3/2), E, blue);
[/asy]
https://latex.artofproblemsolving.com/c/w/o/cwocgeak.png?time=1513823210175
Every line passes through the point, so the intersection of the two graphs consists of exactly
point. The answer is (B).
point. The answer is (B).
See also
| 1970 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 25 |
Followed by Problem 27 | |
| 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 • 31 • 32 • 33 • 34 • 35 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
