Difference between revisions of "1970 AHSME Problems/Problem 26"
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== Solution == | == Solution == | ||
| − | <math>\fbox{B}</math> | + | The graph <math>(x + y - 5)(2x - 3y + 5) = 0</math> is the combined graphs of <math>x + y - 5=0</math> and <math>2x - 3y + 5 = 0</math>. Likewise, the graph <math>(x -y + 1)(3x + 2y - 12) = 0</math> is the combined graphs of <math>x-y+1=0</math> and <math>3x+2y-12=0</math>. All these lines intersect at one point, <math>(2,3)</math>. |
| + | Therefore, the answer is <math>\fbox{(B) 1}</math>. | ||
== See also == | == See also == | ||
Revision as of 21:41, 20 December 2017
Problem
The number of distinct points in the 
-plane common to the graphs of 
and 
is
Solution
The graph 
is the combined graphs of 
and 
. Likewise, the graph 
is the combined graphs of 
and 
. All these lines intersect at one point, 
.
Therefore, the answer is 
.
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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
