The problem asks to solve a system of linear equations using substitution. The two equations are:

$6x - 2y = 10 \quad \text{(Equation 1)}$ $y = 3x - 5 \quad \text{(Equation 2)}$

To use the substitution method, we can substitute the expression for $y$ from Equation 2 into Equation 1.

Step-by-Step Solution:

1. From Equation 2, we know that $y = 3x - 5$.
2. Substitute $y = 3x - 5$ into the first equation $6x - 2y = 10$.

This substitution yields: $6x - 2(3x - 5) = 10$

Now, let's match this with the given options.

Answer:

Option C, $6x - 2(3x - 5) = 10$, correctly represents the first step of substitution.

Would you like more details on how to solve the rest of the system? Also, here are 5 related questions to consider:

1. What is the next step after substituting $y = 3x - 5$ into the first equation?
2. How do you simplify the equation $6x - 2(3x - 5) = 10$?
3. What are the advantages of solving systems of equations using substitution compared to elimination?
4. Can this system of equations be solved using the elimination method?
5. How can graphing help visualize the solution to this system?

Tip: In the substitution method, always solve one equation for a variable first, then substitute that expression into the other equation.