You are given the following system of linear equations:

1. \( x + y = 8 \)
2. \( x - y = 3 \)

To solve this system, let's add the two equations:

\[
(x + y) + (x - y) = 8 + 3
\]

Simplifying both sides:

\[
2x = 11
\]

Now, solve for \( x \):

\[
x = \frac{11}{2} = 5.5
\]

Next, substitute \( x = 5.5 \) into one of the original equations, say \( x + y = 8 \):

\[
5.5 + y = 8
\]

Solve for \( y \):

\[
y = 8 - 5.5 = 2.5
\]

Thus, the solution is:

\[
x = 5.5, \quad y = 2.5
\]

### Do you want more details or have any questions?

Here are 5 related questions to expand on this:
1. How do we verify the solution to a system of equations?
2. What happens if we graph these two equations?
3. Can we solve this system using matrices?
4. How would the solution change if we multiplied one equation by a constant?
5. Can we express the solution as a vector?

**Tip:** Always double-check your solution by substituting it back into the original equations to make sure it satisfies both.

Learn how to solve a system of linear equations x + y = 8 and x - y = 3 step-by-step. Understand the method of elimination to find values of x and y. Suitable for students in Grades 7-9.

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