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Let’s solve this maze step by step using substitution. We start at the “Start” box and follow the path by solving each system of equations, then matching our answer to the coordinate that leads us to the next box — until we reach “Finish”.

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Step 1: Start Box

Equations:
> x = -2y
> 4x + 3y = 10

Substitute x from first equation into second:

4(-2y) + 3y = 10
→ -8y + 3y = 10
→ -5y = 10
→ y = -2

Now plug back to find x:
x = -2(-2) = 4

✔ Solution: (4, -2)

Look for the arrow labeled (4, -2) → it points to the box with:

> y = 4x + 15
> -5x - y = 3

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Step 2: Next Box

Equations:
> y = 4x + 15
> -5x - y = 3

Substitute y from first into second:

-5x - (4x + 15) = 3
→ -5x - 4x - 15 = 3
→ -9x = 18
→ x = -2

Now find y:
y = 4(-2) + 15 = -8 + 15 = 7

✔ Solution: (-2, 7)

Look for arrow labeled (-2, 7) → points to:

> -2x + y = 12
> y = -5x - 9

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Step 3: Next Box

Equations:
> -2x + y = 12
> y = -5x - 9

Substitute y from second into first:

-2x + (-5x - 9) = 12
→ -7x - 9 = 12
→ -7x = 21
→ x = -3

Find y:
y = -5(-3) - 9 = 15 - 9 = 6

✔ Solution: (-3, 6)

Look for arrow labeled (-3, 6) → points to:

> x = 5y + 4
> 3x - 2y = -14

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Step 4: Next Box

Equations:
> x = 5y + 4
> 3x - 2y = -14

Substitute x:

3(5y + 4) - 2y = -14
→ 15y + 12 - 2y = -14
→ 13y = -26
→ y = -2

Find x:
x = 5(-2) + 4 = -10 + 4 = -6

✔ Solution: (-6, -2)

Look for arrow labeled (-6, -2) → points to:

> x = -y - 5
> x = 2y - 2

Wait — both are solved for x? Let’s set them equal:

-y - 5 = 2y - 2
→ -5 + 2 = 2y + y
→ -3 = 3y
→ y = -1

Then x = -(-1) - 5 = 1 - 5 = -4
OR x = 2(-1) - 2 = -2 - 2 = -4 ✔

✔ Solution: (-4, -1)

Look for arrow labeled (-4, -1) → points directly to Finish!

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We made it! The full path is:

Start → (4,-2) → (-2,7) → (-3,6) → (-6,-2) → (-4,-1) → Finish

All steps checked out. No mistakes in substitution or arithmetic.

Final Answer:
The correct path through the maze ends at "Finish" after solving these systems in order:
Start → (4, -2) → (-2, 7) → (-3, 6) → (-6, -2) → (-4, -1) → Finish