To solve a system of equations using substitution, Anthony would first substitute the expression for $y$ from the second equation into the first equation.

Given:

1. $6x - 2y = 10$
2. $y = 3x - 5$

Anthony substitutes $y = 3x - 5$ into the first equation $6x - 2y = 10$.

Substituting for $y$: $6x - 2(3x - 5) = 10$

Thus, the equation that represents the first step is: $\boxed{C. \ 6x - 2(3x - 5) = 10}$

Would you like further explanation on the substitution method or how to continue solving the system?

Related questions:

1. How would you solve the equation after substitution?
2. Can you use elimination to solve the same system of equations?
3. What happens if you get no solution for the system of equations?
4. How would you graph these two equations?
5. What is the difference between substitution and elimination methods?

Tip: Always simplify the equation after substitution to make further steps easier.