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.