The problem asks to solve the system of equations using substitution:

$y = x - 5$ $y = -7x + 3$

Step 1: Substituting for $y$

Since both equations represent $y$, we can substitute $y = x - 5$ into the second equation:

$x - 5 = -7x + 3$

Step 2: Solving for $x$

Now, let's solve this equation for $x$:

$x + 7x = 3 + 5$ $8x = 8$ $x = 1$

Step 3: Substituting $x = 1$ into the first equation

Now that we have $x = 1$, substitute this value back into the first equation to find $y$:

$y = 1 - 5$ $y = -4$

Solution:

The solution to the system is $(1, -4)$.

Would you like a more detailed explanation or have any questions?

Here are some related questions:

1. How do you solve systems of equations using elimination?
2. What happens if the system of equations has no solution?
3. How can you check if your solution to a system is correct?
4. What is the graphical interpretation of solving a system of equations?
5. How does substitution differ from other methods like elimination?

Tip: Always simplify and isolate variables step by step when solving systems of equations.