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To solve the "Systems of Equations Substitution Maze," we need to find the solution $(x, y)$ for each system of equations. The correct answer will lead us to the next box in the maze. Let's trace the path step-by-step from the Start.

Step 1: Start Box

Equations:
1) $x = -2y$
2) $4x + 3y = 10$

Solution:
Substitute equation (1) into equation (2):
$$4(-2y) + 3y = 10$$
$$-8y + 3y = 10$$
$$-5y = 10$$
$$y = -2$$

Now find $x$:
$$x = -2(-2) = 4$$

Answer: $(4, -2)$
Looking at the maze, the path labeled $(4, -2)$ leads to the box containing $x = 3y + 8$ and $x + 4y = 15$.

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Step 2: Second Box

Equations:
1) $x = 3y + 8$
2) $x + 4y = 15$

Solution:
Substitute equation (1) into equation (2):
$$(3y + 8) + 4y = 15$$
$$7y + 8 = 15$$
$$7y = 7$$
$$y = 1$$

Now find $x$:
$$x = 3(1) + 8 = 11$$

Answer: $(11, 1)$
Looking at the maze, the path labeled $(11, 1)$ leads to the box containing $y = -4x - 5$ and $3x + y = -3$.

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Step 3: Third Box

Equations:
1) $y = -4x - 5$
2) $3x + y = -3$

Solution:
Substitute equation (1) into equation (2):
$$3x + (-4x - 5) = -3$$
$$-x - 5 = -3$$
$$-x = 2$$
$$x = -2$$

Now find $y$:
$$y = -4(-2) - 5$$
$$y = 8 - 5$$
$$y = 3$$

Answer: $(-2, 3)$
Looking at the maze, the path labeled $(-2, 3)$ leads to the box containing $y = 3x$ and $y = 7x + 16$.

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Step 4: Fourth Box

Equations:
1) $y = 3x$
2) $y = 7x + 16$

Solution:
Since both equal $y$, set them equal to each other:
$$3x = 7x + 16$$
$$-4x = 16$$
$$x = -4$$

Now find $y$:
$$y = 3(-4) = -12$$

Answer: $(-4, -12)$
Looking at the maze, the path labeled $(-4, -12)$ leads to the box containing $y = 3x - 10$ and $3x + 4y = 5$.

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Step 5: Fifth Box

Equations:
1) $y = 3x - 10$
2) $3x + 4y = 5$

Solution:
Substitute equation (1) into equation (2):
$$3x + 4(3x - 10) = 5$$
$$3x + 12x - 40 = 5$$
$$15x = 45$$
$$x = 3$$

Now find $y$:
$$y = 3(3) - 10$$
$$y = 9 - 10$$
$$y = -1$$

Answer: $(3, -1)$
Looking at the maze, the path labeled $(3, -1)$ leads to the box containing $x = 5y + 4$ and $3x - 2y = -14$.

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Step 6: Sixth Box

Equations:
1) $x = 5y + 4$
2) $3x - 2y = -14$

Solution:
Substitute equation (1) into equation (2):
$$3(5y + 4) - 2y = -14$$
$$15y + 12 - 2y = -14$$
$$13y = -26$$
$$y = -2$$

Now find $x$:
$$x = 5(-2) + 4$$
$$x = -10 + 4$$
$$x = -6$$

Answer: $(-6, 2)$
Looking at the maze, the path labeled $(-6, 2)$ leads to the box containing $x = -y - 5$ and $x = 2y - 2$.

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Step 7: Seventh Box

Equations:
1) $x = -y - 5$
2) $x = 2y - 2$

Solution:
Set the expressions for $x$ equal to each other:
$$-y - 5 = 2y - 2$$
$$-3 = 3y$$
$$y = -1$$

Now find $x$:
$$x = 2(-1) - 2$$
$$x = -2 - 2$$
$$x = -4$$

Answer: $(-4, -1)$
This path leads directly to the Finish box.

Final Answer:
The correct path through the maze is:
(4, -2) $\rightarrow$ (11, 1) $\rightarrow$ (-2, 3) $\rightarrow$ (-4, -12) $\rightarrow$ (3, -1) $\rightarrow$ (-6, 2) $\rightarrow$ (-4, -1)