Let's solve this system of equations:

1. $5x - 2y = 1$
2. $y = 4x + 1$

We'll substitute $y = 4x + 1$ from the second equation into the first equation:

$5x - 2(4x + 1) = 1$

Now, simplify and solve for $x$:

$5x - 8x - 2 = 1$

$-3x - 2 = 1$

$-3x = 3$

$x = -1$

Now that we have $x = -1$, substitute it back into $y = 4x + 1$ to find $y$:

$y = 4(-1) + 1 = -4 + 1 = -3$

Thus, the solution to the system of equations is $x = -1$ and $y = -3$, which corresponds to the ordered pair $(-1, -3)$.

So, the correct answer is:

C. (-1, -3)

Would you like more details on this solution or have any further questions? Here are some related questions:

1. What happens if we solve this system using the substitution method versus the elimination method?
2. Can we solve this system by graphing the equations? How would the graphs look?
3. What is the definition of a simultaneous solution in the context of linear equations?
4. How do you know when to use substitution versus elimination in solving systems of equations?
5. How does this method work if the equations are nonlinear?

Tip: Always check your solution by substituting the values back into the original equations to confirm that they satisfy both equations.