Question

Is the point (-1,2) a solution for the system of linear inequalities x + 4y > 20 and 4y > 6x - 15?

A) Yes
B) No
C) Not enough information to determine
D) The system is inconsistent

Answer 1

The point (-1,2) does not satisfy both inequalities x + 4y > 20 and 4y > 6x - 15 as it only satisfies the second inequality but not the first. Therefore, it is not a solution to the system, and the correct answer is B) No.

Step-by-step explanation:

To determine if the point (-1,2) is a solution for the system of linear inequalities x + 4y > 20 and 4y > 6x - 15, we must plug the point into each inequality to see if the inequalities hold true.

1. For the first inequality x + 4y > 20, substituting x = -1 and y = 2 gives us -1 + 4(2) which simplifies to -1 + 8. This equals 7 which is not greater than 20, so the point does not satisfy this inequality.
2. For the second inequality 4y > 6x - 15, substituting x = -1 and y = 2 gives us 4(2) which simplifies to 8, and 6(-1) - 15 which simplifies to -6 - 15. This equals -21. Since 8 is greater than -21, the point does satisfy this second inequality.

Since the point does not satisfy both inequalities, it is not a solution to the system of inequalities. Therefore, the correct answer is B) No.