The problem asks us to find which of the given ordered pairs are solutions to the equation $7x + 4y = 14$ based on the graph.

1. Problem Description

The problem asks us to find which of the given ordered pairs are solutions to the equation $7x + 4y = 14$ based on the graph.

2. Solution Steps

We need to check each ordered pair to see if it satisfies the equation $7x + 4y = 14$.

* $(-6, 7)$: $7(-6) + 4(7) = -42 + 28 = -14 \ne 14$.

* $(-3, 3)$: $7(-3) + 4(3) = -21 + 12 = -9 \ne 14$.

* $(-1, -2)$: $7(-1) + 4(-2) = -7 - 8 = -15 \ne 14$.

* $(5, 6)$: $7(5) + 4(6) = 35 + 24 = 59 \ne 14$.

* $(2, 0)$: $7(2) + 4(0) = 14 + 0 = 14$.

* $(0, -6)$: $7(0) + 4(-6) = 0 - 24 = -24 \ne 14$.

Therefore, the ordered pair $(2, 0)$ is the only solution.

However, the given analysis result in the image suggests that the equation might have been interpreted as $4y = 5 - 3x$, meaning $3x + 4y = 5$, rather than $7x + 4y = 14$. If that's the case, let's check each ordered pair to see if it satisfies the equation $3x + 4y = 5$.

* $(-6, 7)$: $3(-6) + 4(7) = -18 + 28 = 10 \ne 5$.

* $(-3, 3)$: $3(-3) + 4(3) = -9 + 12 = 3 \ne 5$.

* $(-1, -2)$: $3(-1) + 4(-2) = -3 - 8 = -11 \ne 5$.

* $(5, 6)$: $3(5) + 4(6) = 15 + 24 = 39 \ne 5$.

* $(2, 0)$: $3(2) + 4(0) = 6 + 0 = 6 \ne 5$.

* $(0, -6)$: $3(0) + 4(-6) = 0 - 24 = -24 \ne 5$.

So none of the pairs satisfy this equation either.

Let's assume the analysis result on the right side of the image pertains to the equation $4y = 5 - 3x$. Then, from the analysis, we have:

* (5, -7): $4(-7) = 5 - 3(5) \Rightarrow -28 = 5 - 15 \Rightarrow -28 = -10$, False

* (-5, 5): $4(5) = 5 - 3(-5) \Rightarrow 20 = 5 + 15 \Rightarrow 20 = 20$, True

* (-1, -3): $4(-3) = 5 - 3(-1) \Rightarrow -12 = 5 + 3 \Rightarrow -12 = 8$, False

The analysis on the right also provides the solutions (3, -1), (7, -4), and (-5, 5). We will check these to see if they are on the graph.

Let's check if these solutions satisfy $7x + 4y = 14$.

* (3, -1): $7(3) + 4(-1) = 21 - 4 = 17 \ne 14$

* (7, -4): $7(7) + 4(-4) = 49 - 16 = 33 \ne 14$

* (-5, 5): $7(-5) + 4(5) = -35 + 20 = -15 \ne 14$.

Let's assume the analysis result on the right side of the image pertains to the equation $3x + 4y = 5$. Then, we have:

* (3, -1): $3(3) + 4(-1) = 9 - 4 = 5$

* (7, -4): $3(7) + 4(-4) = 21 - 16 = 5$

* (-5, 5): $3(-5) + 4(5) = -15 + 20 = 5$

The equation in the image is stated as $7x + 4y = 14$. From the given options, only $(2, 0)$ is a solution. The graph of the equation is given, so we can check which points are on the line. We look for points that lie on the line. Based on the graph, we can see the points $(-6, 7)$, $(-3, 3)$, $(-1, -2)$, $(2,0)$, and $(0, -6)$ lie roughly on or near the graph. We are able to compute $7x + 4y = 14$.

* $7(-6) + 4(7) = -42 + 28 = -14 \ne 14$

* $7(-3) + 4(3) = -21 + 12 = -9 \ne 14$

* $7(-1) + 4(-2) = -7 - 8 = -15 \ne 14$

* $7(2) + 4(0) = 14 = 14$

* $7(0) + 4(-6) = -24 \ne 14$.

From visual inspection of the graph, $(-6, 7)$, $(-3, 3)$, $(-1, -2)$ and $(0, -6)$ do not appear to lie on the line.

$(2, 0)$ appears to be on the line.

The graph and the equation $7x + 4y = 14$ imply that only the ordered pair $(2, 0)$ is the solution among the provided choices.

3. Final Answer

(2, 0)