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The given system of equations is:

\[
\begin{cases}
x + y = 17 \\
y = x + 3
\end{cases}
\]

We are asked to solve this system using the substitution method. Let's follow the steps:

### Step 1: Substitute the value of \( y \) from the second equation into the first equation.

From the second equation, we have \( y = x + 3 \). Substituting this into the first equation:

\[
x + (x + 3) = 17
\]

### Step 2: Solve for \( x \).

Simplify the equation:

\[
2x + 3 = 17
\]

Subtract 3 from both sides:

\[
2x = 14
\]

Now, divide both sides by 2:

\[
x = 7
\]

### Step 3: Substitute \( x = 7 \) back into the second equation to find \( y \).

Using \( y = x + 3 \):

\[
y = 7 + 3 = 10
\]

### Solution:

The solution to the system is \( (x, y) = (7, 10) \).

Would you like more details on this solution or have any further questions? Here are some related problems you might want to explore:

1. What happens if you use elimination instead of substitution?
2. Solve the system \( x - y = 5 \) and \( y = 2x - 1 \) by substitution.
3. What is the graphical interpretation of the solution to this system?
4. How would the solution change if the system had been \( x + y = 17 \) and \( y = x - 3 \)?
5. Can substitution always be used to solve linear systems? Why or why not?

**Tip:** Always check your solution by substituting both values into the original equations!

Solve the system of equations using the substitution method: x + y = 17 and y = x + 3.

Learn how to solve the system of linear equations x + y = 17 and y = x + 3 using the substitution method. This example covers key algebraic concepts like substitution and solving for variables. Suitable for students in Grades 6-8.

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