For each answer choice, substitute the $x$ and $y$ values into $4x + y > 9$ and check if it is true. Eliminate any choices that fail this first inequality.

After the first inequality, you may be left with one or more candidates. For those, plug into $y \le 2x - 3$ and see which ones still work.

In Desmos, type y > -4x + 9 to represent $4x + y > 9$ (solve for $y$ first) and then type y <= 2x - 3 to represent $y \le 2x - 3$. You should see a shaded region where the two inequalities overlap.

For each answer choice, type it into Desmos as a point, like (1,4), (2,1), (0,-4), and (3,-2). See which point lies in the overlapping shaded region of both inequalities; that point is the one that satisfies the system.

The system is:

An ordered pair $(x, y)$ satisfies this system only if both inequalities are true when you plug in that $x$ and $y$.

So for each answer choice:

• First check $4x + y > 9$.
• Then check $y \le 2x - 3$.

If either one is false, that choice does not work.

Use $4x + y > 9$.

• Choice A: $(1, 4)$
  $4(1) + 4 = 4 + 4 = 8$, and $8 > 9$ is false.
• Choice B: $(2, 1)$
  $4(2) + 1 = 8 + 1 = 9$, and $9 > 9$ is false (it is equal, not greater).
• Choice C: $(0, -4)$
  $4(0) + (-4) = -4$, and $-4 > 9$ is false.
• Choice D: $(3, -2)$
  $4(3) + (-2) = 12 - 2 = 10$, and $10 > 9$ is true.

So far, only choice D makes the first inequality true; the others already fail the system.

Now check $y \le 2x - 3$ for the remaining candidate from step 2.

• For $(3, -2)$:
  Compute $2x - 3$:

Compare $y$ to this value:

This is true, so $(3, -2)$ satisfies both inequalities.

Therefore, the ordered pair that satisfies the system is $(3, -2)$.