Let’s solve the given system of equations using substitution. The equations are:

1. $y = -8x - 5$
2. $y = -2x + 1$

Step 1: Substitution

Since both equations equal $y$, set them equal to each other: $-8x - 5 = -2x + 1$

Step 2: Solve for $x$

Rearrange to isolate $x$: $-8x + 2x = 1 + 5$ $-6x = 6$ $x = -1$

Step 3: Solve for $y$

Substitute $x = -1$ into one of the original equations. Using $y = -8x - 5$: $y = -8(-1) - 5$ $y = 8 - 5$ $y = 3$

Final Solution:

The solution is: $(x, y) = (-1, 3)$

Let me know if you'd like additional details or clarification!

Here are 5 related questions for you to consider:

1. How would the solution change if the equations were parallel lines instead of intersecting?
2. Can substitution always be used for solving systems of linear equations?
3. How would you solve the system if both equations were in standard form instead of slope-intercept form?
4. What is the graphical interpretation of the solution $(-1, 3)$?
5. How can you verify the solution algebraically?

Tip: Always double-check your solution by substituting $x$ and $y$ into both original equations.