For each row in a table, plug in the $x$ and $y$ values into $2x+3y$ and calculate the result. Then compare that result to $18$.

The symbol is $>$, not $\ge$. A value equal to $18$ does not satisfy $2x+3y>18$.

If even one pair in a table does not satisfy the inequality, you can reject that entire table without checking the remaining rows.

In Desmos, type 2x+3y>18 to graph the solution region for the inequality. The shaded area represents all points $(x,y)$ that satisfy $2x+3y>18$; the boundary line $2x+3y=18$ itself is not included.

For each answer choice, enter its three points as separate expressions, like (3,4), (6,4), (9,2) for one choice. Desmos will show these as dots on the graph.

For each choice, check whether its three points all lie inside the shaded region (not just on the boundary). Any choice with even one point outside the shaded area or exactly on the boundary does not work. The correct table is the one where all three of its points lie strictly inside the shaded region.

The inequality is $2x+3y>18$. A pair $(x,y)$ is a solution only if the value of $2x+3y$ is greater than $18$ when you plug in that $x$ and $y$.

So for each pair in a table:

• Compute $2x+3y$.
• Compare the result to $18$.
• If it is greater than $18$, the pair is a solution.
• If it is equal to or less than $18$, the pair is not a solution.

For a table to be correct, all three pairs in that table must be solutions.

Choice A has the pairs $(3,4)$, $(6,4)$, and $(9,2)$.

• For $(3,4)$: $2(3)+3(4)=6+12=18$. Since $18$ is not greater than $18$, $(3,4)$ is not a solution.
• We could stop here, because one failure means the whole table cannot be correct.

So Choice A cannot be the correct table.

Choice B has the pairs $(3,6)$, $(6,4)$, and $(9,0)$.

• For $(3,6)$: $2(3)+3(6)=6+18=24>18$ ✔
• For $(6,4)$: $2(6)+3(4)=12+12=24>18$ ✔
• For $(9,0)$: $2(9)+3(0)=18+0=18$. Since $18$ is not greater than $18$, $(9,0)$ is not a solution.

Because one pair fails, Choice B cannot be the correct table.

Choice C has the pairs $(3,5)$, $(6,2)$, and $(9,1)$.

• For $(3,5)$: $2(3)+3(5)=6+15=21>18$ ✔
• For $(6,2)$: $2(6)+3(2)=12+6=18$. Since $18$ is not greater than $18$, $(6,2)$ is not a solution.

Again, one non-solution means the whole table is incorrect, so Choice C is eliminated.

The remaining choice, D, has the pairs $(3,5)$, $(6,3)$, and $(9,1)$.

• For $(3,5)$: $2(3)+3(5)=6+15=21>18$ ✔
• For $(6,3)$: $2(6)+3(3)=12+9=21>18$ ✔
• For $(9,1)$: $2(9)+3(1)=18+3=21>18$ ✔

All three pairs satisfy $2x+3y>18$, so Choice D — the table

is the correct answer.