Question

Which ordered pair is a solution of inequalities?

{ y > -2
{x + y <_ 4

A) (-2,-3)
B) (1,3)
C) (1,5)
D) (0,-4)

Answer 1

B is the only solution

Explanation:

These inequalities are shown in the attached picture. Which can be obtained drawing y > -2 (an horizontal line at y=-2, the region is above). and y<= 4-x, a line with a negative slope of -1 and intercept point of 4.

Any ordered pair, located inside the interception between these two regions is a solution of the system.

A. is Outside, below the horizontal line

B. is not clear by graph, hence, lets evaluate it in both inequalities

3>-2 (satisfies)

1+3<=4 (satisfies)

Hence B is a solution.

C. Is outside, we can evaluate it just to make sure:

5>-2 (satisfies)

1+5<= 4 (not true)

Hence C is not a solution.

D. is outside