Difference between revisions of "1955 AHSME Problems/Problem 46"

(Created page with "The graphs of <math>2x+3y-6=0, 4x-3y-6=0, x=2</math>, and <math>y=\frac{2}{3}</math> intersect in: <math>\textbf{(A)}\ \text{6 points}\qquad\textbf{(B)}\ \text{1 point}\qquad...")
 
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<math>y = \frac{2}{3}</math> stays as is
 
<math>y = \frac{2}{3}</math> stays as is
  
We can graph the four lines here:[https://www.desmos.com/calculator/vagsrdsrrc|Desmos]
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We can graph the four lines here:[https://www.desmos.com/calculator/ukceuatbb2]
  
 
When we do that, the answer turns out to be <math>\boxed{\textbf{(B)} \text{1 point}}</math>.
 
When we do that, the answer turns out to be <math>\boxed{\textbf{(B)} \text{1 point}}</math>.
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==See Also==
 
==See Also==
 
Go back to the rest of the [[1955 AHSME Problems]].
 
Go back to the rest of the [[1955 AHSME Problems]].
  
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 16:10, 8 December 2020

The graphs of $2x+3y-6=0, 4x-3y-6=0, x=2$, and $y=\frac{2}{3}$ intersect in:

$\textbf{(A)}\ \text{6 points}\qquad\textbf{(B)}\ \text{1 point}\qquad\textbf{(C)}\ \text{2 points}\qquad\textbf{(D)}\ \text{no points}\\ \textbf{(E)}\ \text{an unlimited number of points}$

Solution

We first convert each of the lines into slope-intercept form ($y = mx + b$):

$2x+3y-6=0 ==> 3y = -2x + 6 ==> y = -\frac{2}{3}x + 2$

$4x - 3y - 6 = 0 ==> 4x - 6 = 3y ==> y = \frac{4}{3}x - 2$

$x = 2$ stays as is.

$y = \frac{2}{3}$ stays as is

We can graph the four lines here:[1]

When we do that, the answer turns out to be $\boxed{\textbf{(B)} \text{1 point}}$.

See Also

Go back to the rest of the 1955 AHSME Problems.

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png