Answer :
To determine which ordered pair satisfies both inequalities
[tex]\[ y > -2x + 3 \][/tex]
[tex]\[ y \leq x - 2 \][/tex]
we need to check each given ordered pair step-by-step.
Let's analyze each pair:
1. Pair (0, 0):
[tex]\[ y = 0, x = 0 \][/tex]
Check the first inequality \( y > -2x + 3 \):
[tex]\[ 0 > -2(0) + 3 \implies 0 > 3 \quad \text{(False)} \][/tex]
Since this pair does not satisfy the first inequality, we can move on to the next pair.
2. Pair (0, -1):
[tex]\[ y = -1, x = 0 \][/tex]
Check the first inequality \( y > -2x + 3 \):
[tex]\[ -1 > -2(0) + 3 \implies -1 > 3 \quad \text{(False)} \][/tex]
Since this pair does not satisfy the first inequality, we can move on to the next pair.
3. Pair (1, 1):
[tex]\[ y = 1, x = 1 \][/tex]
Check the first inequality \( y > -2x + 3 \):
[tex]\[ 1 > -2(1) + 3 \implies 1 > 1 \quad \text{(False)} \][/tex]
Since this pair does not satisfy the first inequality, we can move on to the next pair.
4. Pair (3, 0):
[tex]\[ y = 0, x = 3 \][/tex]
Check the first inequality \( y > -2x + 3 \):
[tex]\[ 0 > -2(3) + 3 \implies 0 > -6 + 3 \implies 0 > -3 \quad \text{(True)} \][/tex]
Now, check the second inequality \( y \leq x - 2 \):
[tex]\[ 0 \leq 3 - 2 \implies 0 \leq 1 \quad \text{(True)} \][/tex]
This pair satisfies both inequalities.
Therefore, the ordered pair that makes both inequalities true is:
[tex]\[ (3, 0) \][/tex]
[tex]\[ y > -2x + 3 \][/tex]
[tex]\[ y \leq x - 2 \][/tex]
we need to check each given ordered pair step-by-step.
Let's analyze each pair:
1. Pair (0, 0):
[tex]\[ y = 0, x = 0 \][/tex]
Check the first inequality \( y > -2x + 3 \):
[tex]\[ 0 > -2(0) + 3 \implies 0 > 3 \quad \text{(False)} \][/tex]
Since this pair does not satisfy the first inequality, we can move on to the next pair.
2. Pair (0, -1):
[tex]\[ y = -1, x = 0 \][/tex]
Check the first inequality \( y > -2x + 3 \):
[tex]\[ -1 > -2(0) + 3 \implies -1 > 3 \quad \text{(False)} \][/tex]
Since this pair does not satisfy the first inequality, we can move on to the next pair.
3. Pair (1, 1):
[tex]\[ y = 1, x = 1 \][/tex]
Check the first inequality \( y > -2x + 3 \):
[tex]\[ 1 > -2(1) + 3 \implies 1 > 1 \quad \text{(False)} \][/tex]
Since this pair does not satisfy the first inequality, we can move on to the next pair.
4. Pair (3, 0):
[tex]\[ y = 0, x = 3 \][/tex]
Check the first inequality \( y > -2x + 3 \):
[tex]\[ 0 > -2(3) + 3 \implies 0 > -6 + 3 \implies 0 > -3 \quad \text{(True)} \][/tex]
Now, check the second inequality \( y \leq x - 2 \):
[tex]\[ 0 \leq 3 - 2 \implies 0 \leq 1 \quad \text{(True)} \][/tex]
This pair satisfies both inequalities.
Therefore, the ordered pair that makes both inequalities true is:
[tex]\[ (3, 0) \][/tex]
