Consider the system of inequalities and its graph. y ≤ –0.75x y ≤ 3x – 2 in which section of the graph does the actual solution to the system lie? a. 1 b. 2 c. 3 d. 4

ANSWER

The actual solution lie in region 4.

EXPLANATION

The given system of inequalities are



Choose a point from each region and substitute in to the system of inequalities, the one that satisfies the system simultaneously is the actual solution.

Region 2: We test for

Thus,




The above statement is false.

For region 1: We test for





The first statement is true but the second statement is false, so the whole thing is false.

For Region 3: We test






The first statement is false and the second is true so the whole statement is not true.

For region 4: We test







Both statements are true, region 4 represents the actual solution to the system.

The correct answer is d. (0,5)