Final answer:
After testing each point in both inequalities of the system, only point B (4,1) satisfies both, making it the correct answer for the system of inequalities given. Option b
Step-by-step explanation:
To determine which of the points satisfies the system of inequalities x - y > 2 and y < 3x - 4, we need to test each point in both inequalities:
For point A (0,0), the first inequality becomes 0 - 0 > 2, which is false, and the second inequality becomes 0 < 3*0 - 4, which is also false. Therefore, point A does not satisfy the system.
For point B (4,1), the first inequality becomes 4 - 1 > 2, which is true, and the second inequality becomes 1 < 3*4 - 4, which is true. Point B satisfies both inequalities.
For point C (0,-3), the first inequality becomes 0 - (-3) > 2, which is true, and the second inequality becomes -3 < 3*0 - 4, which is false. Point C does not satisfy the system.
For point D (5,3), the first inequality becomes 5 - 3 > 2, which is false, and the second inequality becomes 3 < 3*5 - 4, which is true. Point D does not satisfy both inequalities.
Only point B (4,1) satisfies both inequalities in the system, making it the correct answer. option b