To determine which ordered pair \((x, y)\) satisfies both inequalities:
[tex]\[ y > -3x + 3 \][/tex]
[tex]\[ y \geq 2x - 2 \][/tex]
we need to check each pair against both inequalities.
1. Pair (1, 0):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 0 > -3(1) + 3 \rightarrow 0 > 0 \][/tex] (False)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 0 \geq 2(1) - 2 \rightarrow 0 \geq 0 \][/tex] (True)
This pair does not satisfy the first inequality, so (1, 0) is not a solution.
2. Pair (-1, 1):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 1 > -3(-1) + 3 \rightarrow 1 > 6 \][/tex] (False)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 1 \geq 2(-1) - 2 \rightarrow 1 \geq -4 \][/tex] (True)
This pair does not satisfy the first inequality, so (-1, 1) is not a solution.
3. Pair (2, 2):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 2 > -3(2) + 3 \rightarrow 2 > -3 \][/tex] (True)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 2 \geq 2(2) - 2 \rightarrow 2 \geq 2 \][/tex] (True)
This pair satisfies both inequalities, so (2, 2) is a solution.
4. Pair (0, 3):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 3 > -3(0) + 3 \rightarrow 3 > 3 \][/tex] (False)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 3 \geq 2(0) - 2 \rightarrow 3 \geq -2 \][/tex] (True)
This pair does not satisfy the first inequality, so (0, 3) is not a solution.
Thus, the ordered pair [tex]\((2, 2)\)[/tex] makes both inequalities true.
