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]
