To solve the system of linear equations using substitution, Anthony would first substitute the expression for $y$ from the second equation $y = 3x - 5$ into the first equation $6x - 2y = 10$.

Let's substitute $y = 3x - 5$ into the first equation:

$6x - 2(3x - 5) = 10$

This corresponds to option C: $6x - 2(3x - 5) = 10$.

Would you like a detailed breakdown of the solution process or any further clarifications?

Here are 5 related questions you might consider:

1. How do you solve the equation $6x - 2(3x - 5) = 10$?
2. What is the general method for solving systems of equations by substitution?
3. Can you solve this system using the elimination method instead?
4. What are some other methods for solving systems of linear equations?
5. How do you check if your solution to a system of equations is correct?

Tip: When solving by substitution, always substitute the variable's value carefully to avoid mistakes in signs or operations.