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Which point satisfies each of the following inequalities?
x + 4y > -4
2x - y \u2264 3
y < 4

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Question:

A
1212

explanation

1212Two methods can be used to solve this question: 1) graph each of the inequalities then compare the solution set with the answer choices, or 2) substitute each answer choice into the inequalities to test its validity. Method 2 will be used here:
Remember that as soon as an answer choice fails to satisfy one of the inequalities, it cannot be a valid solution. To begin, substituting (0, 4) into the 3rd inequality:
4 < 4, which is not true, so this answer choice is incorrect.
Testing (0, -1):
0 + 4(-1) > -4, which becomes

0 - 4 > -4, or -4 > -4, which is also false, so this answer choice is incorrect.
Testing (3, 1):
2(3) - 1 \u2264 3, which becomes

6 - 1 \u2264 3, or 5 \u2264 3, which is also false, so this answer choice is incorrect.
The remaining answer choice satisfies each inequality:
12 > -4, , and

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