Remember that in an ordered pair $(x, y)$, the first number is $x$ and the second number is $y$. When you substitute, replace $x$ with the first number and $y$ with the second.

Start with the first inequality $3x - y \le 7$ and plug in each answer choice. Eliminate any option that does not make this inequality true, then check the remaining options in the second inequality $y > -2x + 1$.

Be careful with $\le$ versus $>$: $\le$ allows "less than or equal to," but $>$ requires the left side to be strictly greater than the right side, not equal or less.

In Desmos, enter the two boundary lines:

• y = 3x - 7 (this comes from rewriting $3x - y \le 7$ as $y \ge 3x - 7$)
• y = -2x + 1 (from the second inequality).

Replace the equations with the inequalities:

• Type y >= 3x - 7 for $3x - y \le 7$.
• Type y > -2x + 1 for $y > -2x + 1$.

Desmos will shade the regions that satisfy each inequality; the solution set to the system is where the shaded regions overlap.

Plot each option as a point by typing them into Desmos, for example (−1, −2), (3, 0), etc. Look to see which point lies inside the overlapping shaded region (not just on one region). The point that lies in that intersection region is the solution to the system.

A solution to the system must make both inequalities true at the same time:

• $3x - y \le 7$
• $y > -2x + 1$

Each answer choice is an ordered pair $(x, y)$, where the first number is $x$ and the second number is $y$. You need to plug in each pair and check both inequalities.

Use $3x - y \le 7$.

Compute $3x - y$ for each pair:

• A) $(-1, -2)$: $3(-1) - (-2) = -3 + 2 = -1$, and $-1 \le 7$ (works)
• B) $(3, 0)$: $3(3) - 0 = 9$, and $9 \le 7$ is false (fails)
• C) $(2, 2)$: $3(2) - 2 = 6 - 2 = 4$, and $4 \le 7$ (works)
• D) $(0, -6)$: $3(0) - (-6) = 6$, and $6 \le 7$ (works)

So option B is not a solution because it fails the first inequality. A, C, and D still might work.

Now use $y > -2x + 1$ for the options that passed the first check (A, C, and D):

• A) $(-1, -2)$: right side is $-2(-1) + 1 = 2 + 1 = 3$. Check if $-2 > 3$ (this is false).
• C) $(2, 2)$: right side is $-2(2) + 1 = -4 + 1 = -3$. Check if $2 > -3$ (this is true).
• D) $(0, -6)$: right side is $-2(0) + 1 = 1$. Check if $-6 > 1$ (this is false).

Only one of these ordered pairs makes both inequalities true.

From the checks:

• Option A fails the second inequality.
• Option B fails the first inequality.
• Option D fails the second inequality.

The only ordered pair that satisfies both $3x - y \le 7$ and $y > -2x + 1$ is $(2, 2)$.