Answer :
To determine which ordered pair makes both inequalities true, we will test each given pair against the two inequalities:
1. \( y > -3x + 3 \)
2. \( y \geq 2x - 2 \)
We will evaluate each ordered pair \((x, y)\) in these inequalities to find out which pair satisfies both inequalities.
### Testing the pair \((1, 0)\):
1. Check the first inequality: \( y > -3x + 3 \)
[tex]\[ 0 > -3(1) + 3 \][/tex]
[tex]\[ 0 > -3 + 3 \][/tex]
[tex]\[ 0 > 0 \quad \text{(False)} \][/tex]
Since the first inequality is not satisfied, \((1, 0)\) does not make both inequalities true.
### Testing the pair \((-1, 1)\):
1. Check the first inequality: \( y > -3x + 3 \)
[tex]\[ 1 > -3(-1) + 3 \][/tex]
[tex]\[ 1 > 3 + 3 \][/tex]
[tex]\[ 1 > 6 \quad \text{(False)} \][/tex]
Since the first inequality is not satisfied, \((-1, 1)\) does not make both inequalities true.
### Testing the pair \((2, 2)\):
1. Check the first inequality: \( y > -3x + 3 \)
[tex]\[ 2 > -3(2) + 3 \][/tex]
[tex]\[ 2 > -6 + 3 \][/tex]
[tex]\[ 2 > -3 \quad \text{(True)} \][/tex]
2. Check the second inequality: \( y \geq 2x - 2 \)
[tex]\[ 2 \geq 2(2) - 2 \][/tex]
[tex]\[ 2 \geq 4 - 2 \][/tex]
[tex]\[ 2 \geq 2 \quad \text{(True)} \][/tex]
Since both inequalities are satisfied, \((2, 2)\) makes both inequalities true.
### Testing the pair \((0, 3)\):
1. Check the first inequality: \( y > -3x + 3 \)
[tex]\[ 3 > -3(0) + 3 \][/tex]
[tex]\[ 3 > 0 + 3 \][/tex]
[tex]\[ 3 > 3 \quad \text{(False)} \][/tex]
Since the first inequality is not satisfied, \((0, 3)\) does not make both inequalities true.
### Conclusion
The only ordered pair that makes both inequalities true is \((2, 2)\). Therefore, the correct pair is:
[tex]\[ (2, 2) \][/tex]
1. \( y > -3x + 3 \)
2. \( y \geq 2x - 2 \)
We will evaluate each ordered pair \((x, y)\) in these inequalities to find out which pair satisfies both inequalities.
### Testing the pair \((1, 0)\):
1. Check the first inequality: \( y > -3x + 3 \)
[tex]\[ 0 > -3(1) + 3 \][/tex]
[tex]\[ 0 > -3 + 3 \][/tex]
[tex]\[ 0 > 0 \quad \text{(False)} \][/tex]
Since the first inequality is not satisfied, \((1, 0)\) does not make both inequalities true.
### Testing the pair \((-1, 1)\):
1. Check the first inequality: \( y > -3x + 3 \)
[tex]\[ 1 > -3(-1) + 3 \][/tex]
[tex]\[ 1 > 3 + 3 \][/tex]
[tex]\[ 1 > 6 \quad \text{(False)} \][/tex]
Since the first inequality is not satisfied, \((-1, 1)\) does not make both inequalities true.
### Testing the pair \((2, 2)\):
1. Check the first inequality: \( y > -3x + 3 \)
[tex]\[ 2 > -3(2) + 3 \][/tex]
[tex]\[ 2 > -6 + 3 \][/tex]
[tex]\[ 2 > -3 \quad \text{(True)} \][/tex]
2. Check the second inequality: \( y \geq 2x - 2 \)
[tex]\[ 2 \geq 2(2) - 2 \][/tex]
[tex]\[ 2 \geq 4 - 2 \][/tex]
[tex]\[ 2 \geq 2 \quad \text{(True)} \][/tex]
Since both inequalities are satisfied, \((2, 2)\) makes both inequalities true.
### Testing the pair \((0, 3)\):
1. Check the first inequality: \( y > -3x + 3 \)
[tex]\[ 3 > -3(0) + 3 \][/tex]
[tex]\[ 3 > 0 + 3 \][/tex]
[tex]\[ 3 > 3 \quad \text{(False)} \][/tex]
Since the first inequality is not satisfied, \((0, 3)\) does not make both inequalities true.
### Conclusion
The only ordered pair that makes both inequalities true is \((2, 2)\). Therefore, the correct pair is:
[tex]\[ (2, 2) \][/tex]
