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To solve the system of equations by substitution, we have the following system:

\[
\begin{cases}
2x + y = 8 \\
y = x - 7
\end{cases}
\]

### Step 1: Substitute \( y = x - 7 \) into the first equation.
Since we know that \( y = x - 7 \), substitute this into the first equation \( 2x + y = 8 \):

\[
2x + (x - 7) = 8
\]

### Step 2: Simplify the equation.
Combine like terms:

\[
2x + x - 7 = 8
\]

\[
3x - 7 = 8
\]

### Step 3: Solve for \( x \).
Add 7 to both sides:

\[
3x = 15
\]

Now, divide both sides by 3:

\[
x = 5
\]

### Step 4: Substitute \( x = 5 \) back into the equation \( y = x - 7 \).
Now substitute \( x = 5 \) into the second equation:

\[
y = 5 - 7 = -2
\]

### Final Answer:
The solution to the system is \( x = 5 \) and \( y = -2 \).

Would you like further details on any part of the process?

Here are 5 related questions to expand your understanding:
1. How would the solution change if the second equation was \( y = 7 - x \)?
2. Can substitution always be used to solve systems of equations?
3. What are other methods to solve systems of equations besides substitution?
4. How do we graphically interpret the solution of this system?
5. What happens if the two equations in the system are parallel?

**Tip:** When using substitution, always simplify the substituted equation carefully to avoid mistakes.

Learn how to solve the system of equations 2x + y = 8 and y = x - 7 using the substitution method. Follow a detailed step-by-step approach, including substitution, simplification, and solving for variables. This problem is suitable for students in Grades 8-10.

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