The image shows a math problem involving a system of equations with two variables, represented by a square and a triangle. The equations are:

$\text{Square} - \text{Triangle} = 4$ $\text{Square} + \text{Triangle} = 12$

Let's solve this system step by step.

Step 1: Set up the equations

Let's denote:

• The square by $x$
• The triangle by $y$

So, the system of equations becomes:

$x - y = 4 \quad \text{(Equation 1)}$ $x + y = 12 \quad \text{(Equation 2)}$

Step 2: Solve by Addition

Add Equation 1 and Equation 2:

$(x - y) + (x + y) = 4 + 12$ $2x = 16$ $x = \frac{16}{2} = 8$

So, the value of the square $x$ is 8.

Step 3: Substitute $x = 8$ into one of the original equations

Substitute $x = 8$ into Equation 1:

$8 - y = 4$ $y = 8 - 4 = 4$

So, the value of the triangle $y$ is 4.

Final Answer:

• The square is 8.
• The triangle is 4.

Would you like more details or have any questions?

Here are five related questions for further exploration:

1. How would the solution change if the system of equations were different?
2. Can you solve the system using substitution instead of addition?
3. How can you represent the solution graphically?
4. What happens if you subtract Equation 2 from Equation 1?
5. What if the equations had different coefficients for the square and triangle?

Tip: When solving a system of equations, combining equations by addition or subtraction is a quick way to eliminate one of the variables and simplify the problem.