square * square + circle == 16
triangle * triangle * triangle == 27
triangle * square == 6

Let's break down the system of equations involving the square, circle, and triangle.

We have the following equations:

1. \( \text{square}^2 + \text{circle} = 16 \)
2. \( \text{triangle}^3 = 27 \)
3. \( \text{triangle} \times \text{square} = 6 \)

Let's solve these step by step.

### Step 1: Solve for the triangle
From the second equation:
\[
\text{triangle}^3 = 27
\]
Taking the cube root of both sides:
\[
\text{triangle} = \sqrt[3]{27} = 3
\]

### Step 2: Solve for the square
Now, using the value of the triangle in the third equation:
\[
\text{triangle} \times \text{square} = 6
\]
Substitute \( \text{triangle} = 3 \):
\[
3 \times \text{square} = 6
\]
Divide by 3:
\[
\text{square} = \frac{6}{3} = 2
\]

### Step 3: Solve for the circle
Using the value of the square in the first equation:
\[
\text{square}^2 + \text{circle} = 16
\]
Substitute \( \text{square} = 2 \):
\[
2^2 + \text{circle} = 16
\]
\[
4 + \text{circle} = 16
\]
Subtract 4 from both sides:
\[
\text{circle} = 16 - 4 = 12
\]

### Final Answer
- **Square** = 2
- **Circle** = 12
- **Triangle** = 3

Would you like any further details or have any questions?

Here are some related questions you might find interesting:
1. What happens if you change the second equation to \( \text{triangle}^3 = 64 \)?
2. How would the solution change if \( \text{triangle} \times \text{square} = 12 \) instead?
3. What if the first equation was \( \text{square}^2 + \text{circle} = 25 \)?
4. Can we have multiple solutions if we modify the equations slightly?
5. How would you solve this system if \( \text{triangle}^3 \) had a negative value?

**Tip:** Always start with the simplest equation or the one that involves only one variable to make solving systems of equations easier.

Learn how to solve a system of equations involving squares, circles, and triangles with step-by-step solutions. This problem covers key algebraic concepts and equations including squares, cubes, and multiplication. Suitable for students in Grades 7-9.

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