1955 AMC 12 Problem 46

Question

The graphs of

2x+3y-6=0,

4x-3y-6=0,

x=2,

and

y=\dfrac23

intersect in:

6

points

1

point

2

points

no points

an unlimited number of points

Solve the first two linear equations simultaneously

Check whether that solution also satisfies each of the last two displayed equations

Adding the first two equations gives

6x-12=0,

so

x=2.

Substitution gives

3y=2,

hence

y=\frac{2}{3}.

This point also lies on the last two given lines. Therefore all four graphs have the single common point

(2,\frac{2}{3}).

Thus, the correct answer is B.

Problem 46 in other years