To solve this system of equations using substitution, we can follow these steps:

1. Substitute $y = -2x - 7$ into the second equation.

   The system is: $y = -2x - 7$ $2y - x = 1$

2. Substitute $y$ from the first equation into the second equation: $2(-2x - 7) - x = 1$

3. Simplify the equation: $-4x - 14 - x = 1$ Combine like terms: $-5x - 14 = 1$ Add 14 to both sides: $-5x = 15$ Divide by -5: $x = -3$

4. Substitute $x = -3$ back into the first equation to find $y$: $y = -2(-3) - 7$ Simplify: $y = 6 - 7$ $y = -1$

5. Solution: The solution to the system is $(-3, -1)$.

Answer:

D. $(-3, -1)$

Would you like more details on any part of this solution?

---

Here are five related questions for further practice:

1. How would you solve a similar system if the equations were $y = 3x + 4$ and $y = x - 2$?
2. What is the elimination method, and how does it differ from substitution in solving systems?
3. How can we verify that $(-3, -1)$ is the correct solution for this system?
4. What are the steps if both equations in a system are given in terms of $y$?
5. How do we interpret a system of equations that has no solutions?

Tip: Always check your solution by substituting the values back into both original equations. This helps confirm that your answer satisfies both conditions.