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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?

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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.

Solve the system of equations: y = x - 5, y = -7x + 3 using substitution.

Learn how to solve the system of linear equations y = x - 5 and y = -7x + 3 using substitution. This step-by-step solution covers key algebraic concepts such as substitution and solving for variables. Suitable for students in Grades 7-9.

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