Final answer:
Option A, (-2, -4), is the correct solution to the system of inequalities because when substituted into both inequalities, the resulting expressions are true, satisfying the conditions of the system.
Step-by-step explanation:
The question asks to determine which of the options is a solution to the system of inequalities 3x - y > -1 and x - 2y > 4. To figure this out, we need to substitute the x and y values from each option into both inequalities and check whether both inequalities are satisfied.
- Substitute (-2, -4) into both inequalities: 3(-2) - (-4) > -1 becomes -6 + 4 > -1, which simplifies to -2 > -1 (true); and -2 - 2(-4) > 4 becomes -2 + 8 > 4, which simplifies to 6 > 4 (true). So A, (-2, -4), satisfies both inequalities.
- Check other options in the same manner, if needed.
Therefore, option A, (-2, -4), is the correct answer as it is the solution to the system of inequalities.