Question

Algebraically, an ordered pair is a solution to a system of two linear inequalities if and only if it __________.

A.
makes both the top and bottom inequalities false
B.
makes the top inequality true and the bottom inequality false
C.
makes the top inequality false and the bottom inequality true
D.
makes both the top and bottom inequalities true

Answer 1

D. Makes both the top and bottom inequalities true

Explanation:

System of linear inequalities

Consider these two inequalities:

2x+3y > 20

3x-2y > 5

The solution of the system consists of all the ordered pairs (x,y) that satisfy both inequalities. The ordered pair (3,5) makes the first inequality true because

2*3+3*5=21 and it's effectively greater than 20.

But that pair makes the second inequality false, since

3*3-2*5=-1 is not greater than 5.

Thus, the pair (3,5) is not part of the solution.

If we test the pair (6,2), we'll check both inequalities are true, thus (6,2) is part of the solution.

Thus, the correct answer to the question is

D. Makes both the top and bottom inequalities true