https://file.aiquickdraw.com/mathbot/file/17254131005512w0ephz8.jpg

The image contains a system of linear equations:

\[
\begin{cases}
x + y = 12 \\
x - y = 2
\end{cases}
\]

To solve this system, we can use either the substitution method or the elimination method. I'll use the elimination method here.

1. **Add the two equations together** to eliminate \(y\):

\[
(x + y) + (x - y) = 12 + 2
\]

This simplifies to:

\[
2x = 14
\]

So,

\[
x = \frac{14}{2} = 7
\]

2. **Substitute \(x = 7\)** into the first equation \(x + y = 12\) to find \(y\):

\[
7 + y = 12
\]

Subtract 7 from both sides:

\[
y = 12 - 7 = 5
\]

Thus, the solution to the system is:

\[
x = 7, \quad y = 5
\]

Would you like any further details or explanations? Here are some additional related questions:

1. How can the substitution method be used to solve this system?
2. What is the geometric interpretation of the solution?
3. How can you verify the solution is correct?
4. What are some other methods for solving systems of linear equations?
5. What happens if the system of equations is dependent?

**Tip:** When using the elimination method, it's helpful to add or subtract the equations directly if they are already set up to cancel out one of the variables.

Solve the system of linear equations: x + y = 12, x - y = 2.

Learn how to solve the system of linear equations x + y = 12 and x - y = 2 using the elimination method. This problem covers fundamental algebraic concepts and is suitable for students in Grades 6-8.

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