Given the system of equations:

\[
\begin{aligned}
a + b &= 5 \quad \text{(Equation 1)} \\
a - b &= 5 \quad \text{(Equation 2)}
\end{aligned}
\]

We are asked to find \((a - b)^2\).

### Step 1: Solving for \(a - b\)
From Equation 2, we already have:

\[
a - b = 5
\]

### Step 2: Squaring the expression \(a - b\)
Now, we square both sides of the equation:

\[
(a - b)^2 = 5^2 = 25
\]

So, \((a - b)^2 = 25\).

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What are the values of \(a\) and \(b\)?
2. How would you solve for \(a^2 - b^2\)?
3. What would happen if \(a + b\) were a different value?
4. Can you solve the same problem using a different method?
5. What is the geometric interpretation of the system of equations?

**Tip:** When dealing with systems of equations, checking if they can be combined or manipulated directly often simplifies the problem.

Explore how to solve a system of linear equations, where a + b = 5 and a - b = 5. Step-by-step solution provided, including squaring a number. Suitable for Grades 7-9 students.

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