Systems of Equations Substitution Maze | Worksheet - Free Printable

Since I can't view or access images directly, I can’t see the specific maze or equations in your uploaded image. However, based on the description and common structure of such worksheets, I can guide you through how to solve a "Systems of Equations Substitution Maze" step by step.

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🧩 What is this maze?

This worksheet presents a maze where:
- You start at the “Start” box.
- Each box contains a system of two equations.
- You must solve the system using substitution.
- The solution (ordered pair) will tell you which path to take.
- You follow the correct answers until you reach “Finish.”

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✔ Step-by-Step Strategy

#### 🔹 Step 1: Understand the goal
Solve each system of equations using substitution.
- One equation will be solved for one variable (e.g., `y = ...`), or you’ll need to solve it first.
- Plug that expression into the other equation.
- Solve for the remaining variable.
- Back-substitute to find the second variable.
- Write the solution as an ordered pair `(x, y)`.

#### 🔹 Step 2: Use the answer to move through the maze
Each box has a system and possible next paths labeled with coordinate pairs like `(4, -2)` or `(3, 1)`.
After solving the system, your answer should match one of the coordinates on the arrows leading from that box. That tells you which direction to go.

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📌 Example Problem (Illustrative)

Let’s say one box has:

```
System:
1) x + y = 8
2) 4x - 2y = 10
```

#### Solve using substitution:

Step 1: Solve one equation for one variable.
From (1):
`x + y = 8` → `x = 8 - y`

Step 2: Substitute into the second equation:
```
4(8 - y) - 2y = 10
32 - 4y - 2y = 10
32 - 6y = 10
-6y = -22
y = 22/6 = 11/3 ≈ 3.67
```

Wait — this gives a fractional value. But most mazes use integer solutions.

Let’s try another example that's more likely:

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✔ Realistic Example

Box:
```
x = y + 5
4x - 2y = 10
```

Step 1: Since `x = y + 5`, substitute into the second equation:

```
4(y + 5) - 2y = 10
4y + 20 - 2y = 10
2y + 20 = 10
2y = -10
y = -5
```

Now plug back:
`x = y + 5 = -5 + 5 = 0`

So the solution is: (0, -5)

👉 If one of the arrows from this box points to `(0, -5)`, then you follow that path.

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🛠️ Tips for Solving the Maze

1. Always double-check your work.
2. Write down steps neatly — especially when substituting.
3. Look for easy-to-solve systems (like ones already solved for x or y).
4. Use scratch paper to avoid confusion.
5. Only move if your answer matches a labeled coordinate.

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🚀 How to Complete the Maze

1. Start at “Start.”
2. Solve the system.
3. Find the arrow pointing to the correct solution (e.g., `(4, -2)`).
4. Move to that box.
5. Repeat until you reach “Finish.”

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❓ Can I help you solve it?

If you can type out the systems of equations in order (or describe the maze layout), I can:
- Help solve each system.
- Guide you through the correct path.
- Show you how to substitute correctly.

Just list the systems from the start onward, or describe the connections.

For now, here’s a template of what to do:

> Example Path:
>
> Start → (system: x + y = 8, 4x - 2y = 10) → solve → (x=5, y=3) → follow arrow to (5,3) → next system...

Let me know how you'd like to proceed!