Which of the following is a solution to the following system of inequalities?
y > 2x - 1
y ≤ -2x + 3
A (1,1)
B (1, 3)
C (-1,-2)
D (3, -3)
Let's evaluate each option to find which one satisfies both of the inequalities.
Option A: (1,1)
For the first inequality, y > 2x - 1:
1 > 2(1) - 1
1 > 2 - 1
1 > 1 (This is not true, so option A does not satisfy the first inequality.)
Option B: (1, 3)
For the first inequality, y > 2x - 1:
3 > 2(1) - 1
3 > 2 - 1
3 > 1 (This is true.)
For the second inequality, y ≤ -2x + 3:
3 ≤ -2(1) + 3
3 ≤ -2 + 3
3 ≤ 1 (This is not true, so option B does not satisfy the second inequality.)
Option C: (-1,-2)
For the first inequality, y > 2x - 1:
-2 > 2(-1) - 1
-2 > -2 - 1
-2 > -3 (This is true.)
For the second inequality, y ≤ -2x + 3:
-2 ≤ -2(-1) + 3
-2 ≤ 2 + 3
-2 ≤ 5 (This is true.)
Since option C satisfies both inequalities, we don't need to check Option D, as we've found a solution. However, let's check Option D for completeness:
Option D: (3, -3)
For the first inequality, y > 2x - 1:
-3 > 2(3) - 1
-3 > 6 - 1
-3 > 5 (This is not true, so option D does not satisfy the first inequality.)
Therefore, the solution to the system of inequalities is:
C (-1, -2)