To identify which pairs [tex]\((a, y)\)[/tex] satisfy the equation [tex]\(a + 3y = 9\)[/tex], we will check each given option step-by-step.
1. Checking the pair [tex]\((0, 3)\)[/tex]:
[tex]\[
a = 0, \quad y = 3
\][/tex]
Substitute these values into the equation:
[tex]\[
0 + 3 \cdot 3 = 0 + 9 = 9
\][/tex]
Since this is true, [tex]\((0, 3)\)[/tex] is a solution.
2. Checking the pair [tex]\((6, 1)\)[/tex]:
[tex]\[
a = 6, \quad y = 1
\][/tex]
Substitute these values into the equation:
[tex]\[
6 + 3 \cdot 1 = 6 + 3 = 9
\][/tex]
Since this is true, [tex]\((6, 1)\)[/tex] is a solution.
3. Checking the pair [tex]\((-3, -3)\)[/tex]:
[tex]\[
a = -3, \quad y = -3
\][/tex]
Substitute these values into the equation:
[tex]\[
-3 + 3 \cdot (-3) = -3 - 9 = -12
\][/tex]
Since this is not true, [tex]\((-3, -3)\)[/tex] is not a solution.
After verifying each pair, the solutions to the equation [tex]\(a + 3y = 9\)[/tex] are:
[tex]\[
(0, 3) \quad \text{and} \quad (6, 1)
\][/tex]
So the correct answers are:
- [tex]\((0, 3)\)[/tex]
- [tex]\((6, 1)\)[/tex]
