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Sagot :
To determine which ordered pairs [tex]\((x, y)\)[/tex] are solutions to the inequality [tex]\(2y - x \leq -6\)[/tex], we will substitute each pair into the inequality and check if the inequality holds.
Let's test each pair one by one:
1. For [tex]\((-3, 0)\)[/tex]:
[tex]\[ 2(0) - (-3) \leq -6 \][/tex]
Simplifying,
[tex]\[ 0 + 3 \leq -6 \implies 3 \leq -6 \quad \text{(False)} \][/tex]
2. For [tex]\((0, -3)\)[/tex]:
[tex]\[ 2(-3) - 0 \leq -6 \][/tex]
Simplifying,
[tex]\[ -6 \leq -6 \quad \text{(True)} \][/tex]
3. For [tex]\((2, -2)\)[/tex]:
[tex]\[ 2(-2) - 2 \leq -6 \][/tex]
Simplifying,
[tex]\[ -4 - 2 \leq -6 \implies -6 \leq -6 \quad \text{(True)} \][/tex]
4. For [tex]\((6, 1)\)[/tex]:
[tex]\[ 2(1) - 6 \leq -6 \][/tex]
Simplifying,
[tex]\[ 2 - 6 \leq -6 \implies -4 \leq -6 \quad \text{(False)} \][/tex]
5. For [tex]\((1, -4)\)[/tex]:
[tex]\[ 2(-4) - 1 \leq -6 \][/tex]
Simplifying,
[tex]\[ -8 - 1 \leq -6 \implies -9 \leq -6 \quad \text{(True)} \][/tex]
Thus, the ordered pairs that satisfy the inequality [tex]\(2y - x \leq -6\)[/tex] are:
[tex]\[ (0, -3), (2, -2), (1, -4) \][/tex]
Let's test each pair one by one:
1. For [tex]\((-3, 0)\)[/tex]:
[tex]\[ 2(0) - (-3) \leq -6 \][/tex]
Simplifying,
[tex]\[ 0 + 3 \leq -6 \implies 3 \leq -6 \quad \text{(False)} \][/tex]
2. For [tex]\((0, -3)\)[/tex]:
[tex]\[ 2(-3) - 0 \leq -6 \][/tex]
Simplifying,
[tex]\[ -6 \leq -6 \quad \text{(True)} \][/tex]
3. For [tex]\((2, -2)\)[/tex]:
[tex]\[ 2(-2) - 2 \leq -6 \][/tex]
Simplifying,
[tex]\[ -4 - 2 \leq -6 \implies -6 \leq -6 \quad \text{(True)} \][/tex]
4. For [tex]\((6, 1)\)[/tex]:
[tex]\[ 2(1) - 6 \leq -6 \][/tex]
Simplifying,
[tex]\[ 2 - 6 \leq -6 \implies -4 \leq -6 \quad \text{(False)} \][/tex]
5. For [tex]\((1, -4)\)[/tex]:
[tex]\[ 2(-4) - 1 \leq -6 \][/tex]
Simplifying,
[tex]\[ -8 - 1 \leq -6 \implies -9 \leq -6 \quad \text{(True)} \][/tex]
Thus, the ordered pairs that satisfy the inequality [tex]\(2y - x \leq -6\)[/tex] are:
[tex]\[ (0, -3), (2, -2), (1, -4) \][/tex]
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