Final answer:
To solve the linear inequality, y is isolated on one side resulting in y > x + 6. The points are then checked against this inequality, but without the complete system of inequalities provided, a definitive solution cannot be determined from the options given.
Step-by-step explanation:
To find the solution to the system of linear inequalities 3y - x > 2y + 6, we first need to isolate y on one side. By subtracting 2y from both sides, we get y - x > 6. Then, we isolate y completely by adding x to both sides, which gives us y > x + 6. Now we can evaluate which point is a solution to this inequality.
- For point a (-4, -2), -2 is not greater than -4 + 6, so this is not a solution.
- For point b (-6, 8), 8 is greater than -6 + 6, so this is a solution.
- For point c (-2, 10), 10 is greater than -2 + 6, so this could also be a solution.
- For point d (12, -2), -2 is not greater than 12 + 6, so this is not a solution.
However, we only have one system of inequality here when the question implies there should be more. Since the information provided is insufficient to properly answer the question, we cannot determine a correct answer from the choices provided without the complete system of inequalities. Please provide the full system for a definitive solution.