https://file.aiquickdraw.com/mathbot/file/17289242540556eeanam2.jpg

Let's solve the given system of equations using substitution.

The system of equations is:
\[
2x + 3y = 17 \quad \text{(Equation 1)}
\]
\[
x = 2y - 9 \quad \text{(Equation 2)}
\]

### Step 1: Substitute Equation 2 into Equation 1
Since \( x = 2y - 9 \), substitute this expression for \( x \) in Equation 1:
\[
2(2y - 9) + 3y = 17
\]

### Step 2: Simplify the equation
Expand the terms:
\[
4y - 18 + 3y = 17
\]
Combine like terms:
\[
7y - 18 = 17
\]

### Step 3: Solve for \( y \)
Add 18 to both sides:
\[
7y = 35
\]
Now divide by 7:
\[
y = 5
\]

### Step 4: Substitute \( y = 5 \) back into Equation 2
Now that we know \( y = 5 \), substitute it into Equation 2 to solve for \( x \):
\[
x = 2(5) - 9
\]
\[
x = 10 - 9 = 1
\]

### Solution:
The solution to the system is:
\[
x = 1, \quad y = 5
\]

Would you like more details on any step? Let me know if you have any questions!

Here are 5 related questions to expand your understanding:
1. What would happen if we solved this system using the elimination method instead of substitution?
2. How can you verify that the solution \(x = 1\) and \(y = 5\) satisfies both equations?
3. What would the graphical representation of these equations look like?
4. How do you handle systems with no solutions or infinitely many solutions?
5. How would the process change if you were given a nonlinear system of equations?

**Tip:** Always substitute the solution back into both equations to ensure that it satisfies the entire system!

Use substitution to solve the system: 2x + 3y = 17 and x = 2y - 9

Learn how to solve the system of linear equations 2x + 3y = 17 and x = 2y - 9 using the substitution method. Follow the step-by-step solution to find the values of x and y. This topic is essential for students learning algebra and systems of equations, suitable for Grades 8-10.

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