The question is asking to find the value of $3x - y$ given the system of equations:

$-4x + y = 7$ $x + 2y = 5$

We will solve this system of equations and find the value of $3x - y$.

Step 1: Solve the system of equations

We have the two equations:

1. $-4x + y = 7$
2. $x + 2y = 5$

From equation (1), we can express $y$ in terms of $x$: y = 7 + 4x \tag{1}

Substitute this into equation (2): $x + 2(7 + 4x) = 5$ Simplify and solve for $x$: $x + 14 + 8x = 5$ $9x + 14 = 5$ $9x = 5 - 14$ $9x = -9$ $x = -1$

Step 2: Find $y$

Now substitute $x = -1$ into equation (1) to find $y$: $y = 7 + 4(-1)$ $y = 7 - 4 = 3$

Step 3: Find $3x - y$

Now that we have $x = -1$ and $y = 3$, substitute these values into $3x - y$: $3x - y = 3(-1) - 3 = -3 - 3 = -6$

Thus, the value of $3x - y$ is $-6$.

The correct answer is: $\boxed{b. -6}$

Would you like more details or have any questions? Here are some related questions you could explore:

1. What are the steps for solving systems of equations by substitution?
2. Can systems of linear equations always be solved using substitution?
3. What happens if a system of linear equations has no solutions?
4. How can you verify the solution of a system of equations?
5. How does the elimination method differ from substitution in solving systems?

Tip: Always double-check your solutions by substituting them back into the original equations.