Final answer:
The solution for the question from the given option is option C. To determine which of the ordered pairs is a solution to the system of inequalities, we need to substitute the values of x and y into both inequalities and check if the inequalities are satisfied.
Step-by-step explanation:
To determine which of the ordered pairs is a solution to the system of inequalities, we need to substitute the values of x and y into both inequalities and check if the inequalities are satisfied.
- For the first inequality y < 2x, let's check each ordered pair:
- For A: (-2,2)
2 < 2*(-2) -> 2 < -4
This is not true, so A is not a solution. - For B: (0,2)
2 < 2*0 -> 2 < 0
This is not true, so B is not a solution. - For C: (2,2)
2 < 2*2 -> 2 < 4
This is true, so C is a solution. - For D: (0,4)
4 < 2*0 -> 4 < 0
This is not true, so D is not a solution.
- For the second inequality 3x + y > 4, let's check each ordered pair:
- For A: (-2,2)
3*(-2) + 2 > 4 -> -6 + 2 > 4
This is not true, so A is not a solution. - For B: (0,2)
3*0 + 2 > 4 -> 2 > 4
This is not true, so B is not a solution. - For C: (2,2)
3*2 + 2 > 4 -> 6 + 2 > 4
This is true, so C is a solution. - For D: (0,4)
3*0 + 4 > 4 -> 4 > 4
This is not true, so D is not a solution.
Based on our calculations, the ordered pair (2,2) is the only one that satisfies both inequalities, making it the solution to the system.