To solve the system of equations:

\[
y = 2x + 9 \quad \text{(Equation 1)}
\]
\[
y = 4x - 9 \quad \text{(Equation 2)}
\]

### Step 1: Set the equations equal to each other
Since both equations are equal to \( y \), we can set them equal to each other:

\[
2x + 9 = 4x - 9
\]

### Step 2: Solve for \( x \)
Subtract \( 2x \) from both sides:

\[
9 = 2x - 9
\]

Next, add 9 to both sides:

\[
18 = 2x
\]

Finally, divide by 2:

\[
x = 9
\]

### Step 3: Solve for \( y \)
Substitute \( x = 9 \) into one of the original equations, let's use Equation 1:

\[
y = 2(9) + 9 = 18 + 9 = 27
\]

### Solution
The solution to the system of equations is:

\[
x = 9, \quad y = 27
\]

Would you like more details or have any questions? Here are some related problems you might find interesting:

1. Solve the system of equations \(y = 3x + 2\) and \(y = -x + 4\).
2. Find the point of intersection for \(y = 5x + 1\) and \(y = -2x - 7\).
3. Solve the system \(2x - y = 3\) and \(4x + y = 11\).
4. Determine the solution for \(y = x^2 + 4\) and \(y = 2x + 5\).
5. Solve the equations \(3x - 2y = 12\) and \(x + 5y = 7\).

**Tip:** When solving a system of equations by substitution, always make sure that the equations are simplified as much as possible before substituting values.

Learn how to solve the system of equations y=2x+9 and y=4x-9 using the substitution method with a detailed step-by-step solution. Suitable for Grades 7-9 students studying linear equations and systems of equations.

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