To solve the given system of equations:

1. $y - x = 0$
2. $2x - 5y = 9$

Step 1: Solve for one variable from the first equation

From $y - x = 0$, we can rewrite this as: $y = x$

Step 2: Substitute $y = x$ into the second equation

Substituting $y = x$ into $2x - 5y = 9$: $2x - 5(x) = 9$ $2x - 5x = 9$ $-3x = 9$ $x = -3$

Step 3: Solve for $y$ using $y = x$

Since $y = x$, substitute $x = -3$: $y = -3$

Final Solution:

$x = -3, \, y = -3$

Let me know if you'd like a more detailed explanation or if you have any questions!

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Here are 5 related questions for further practice:

1. Solve the system: $x + y = 7$ and $3x - y = 5$.
2. Solve the system: $y = 2x + 1$ and $4x - y = 3$.
3. Find the solution to $x - 2y = 4$ and $3x + y = -5$.
4. How can substitution be used in solving systems of equations?
5. What happens when a system of equations has no solution?

Tip: Always double-check your substitution to ensure accuracy in solving systems of equations.