Final answer:
Points (3, 2) and (2, 3) satisfy both inequalities 2x+3y≥12 and 4x+6y>-6, thus they are both in the solution set. Points (-1, 2) and (0, 0) do not satisfy both inequalities, thus are not in the solution set.
Step-by-step explanation:
The question involves determining which point is in the solution set of a system of inequalities: 2x+3y≥12 and 4x+6y>-6. To solve, each point must be tested in both inequalities to see if it satisfies them.
- For point (3, 2), the inequalities are 2(3)+3(2)≥12 and 4(3)+6(2)>-6, which simplifies to 12≥12 and 24>-6. Both are true, so point (3, 2) satisfies both inequalities.
- For point (2, 3), we get 2(2)+3(3)≥12 and 4(2)+6(3)>-6 which simplifies to 13≥12 and 28>-6. Both are true, so point (2, 3) also satisfies both inequalities.
- For point (-1, 2), the inequalities are 2(-1)+3(2)≥12 and 4(-1)+6(2)>-6, which simplifies to 4≥12 and 8>-6. The first is not true, so point (-1, 2) does not satisfy both inequalities.
- For point (0, 0), we get 2(0)+3(0)≥12 and 4(0)+6(0)>-6 which simplifies to 0≥12 and 0>-6. The first is not true, so point (0, 0) does not satisfy both inequalities.
Points (3, 2) and (2, 3) satisfy both inequalities and are on the solution set.