The given system of equations is:

\[
\begin{aligned}
2y - x &= 0, \\
x &= y + 7.
\end{aligned}
\]

To solve this system, we'll use substitution since the second equation already gives us \( x \) in terms of \( y \).

### Step 1: Substitute \( x = y + 7 \) into the first equation.
Substitute \( x = y + 7 \) into \( 2y - x = 0 \):

\[
2y - (y + 7) = 0.
\]

### Step 2: Simplify the equation.
Distribute and combine like terms:

\[
2y - y - 7 = 0,
\]

\[
y - 7 = 0.
\]

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

\[
y = 7.
\]

### Step 4: Solve for \( x \).
Now that we know \( y = 7 \), substitute this back into the equation \( x = y + 7 \):

\[
x = 7 + 7 = 14.
\]

### Solution:
The solution to the system of equations is \( x = 14 \) and \( y = 7 \).

Would you like to explore further details on the solution or see how the equations graphically intersect? Here are some related questions you might consider:

1. What does the point \( (14, 7) \) represent in the context of this system?
2. How would the solution change if the second equation was \( x = y - 7 \) instead?
3. Can this system be solved graphically? What would the lines look like?
4. How does substitution compare to elimination for solving this system?
5. What if we reversed the roles of \( x \) and \( y \) in the system?

**Tip:** Always substitute your solution back into the original equations to verify it satisfies both equations.

Learn how to solve the system of equations 2y - x = 0 and x = y + 7 with a detailed step-by-step solution. This problem involves using the substitution method to find values of x and y. Suitable for students in Grades 9-12.

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