Q:

Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system? The graph represents the system of inequalities: A. 3x+2y is less than or equal to 3 and 3x+4y is greater than or equal to 2. B. 3x+2y is less than 3 and 3x+4y is greater than 2. C. 3x+2y is greater than 3 and 3x+4y is less than 2. D. 3x2y is greater than or equal to 3 and 3x+4y is less than or equal to 2. The test point ____[(-2,3), (-1,1), (0,2), or (1,1)] satisfies both of the inequalities in the system represented by the graph.

Accepted Solution

A:
The answer is A , and the only test point that satisfies both inequalities in the system is (-2,3)

When 3x + 2y = 3 ,
2y = -3x + 3
y = -3/2 x + 3/2

When 3x + 4y = 2 ,
4y = -3x + 2
y = -3/4 x + 1/2
Since there is no any dashed line appeared on the graph ,
y 《 -3/2 x + 3/2 (1st line)
y 》 -3/4 x + 1/2 (2nd line)
So the answer is A
For the second part, (-2,3) is the only test point that was located in the region between these two lines , the rest of the points were located outside the region causing them couldn't satisfy both inequalities.