https://file.aiquickdraw.com/mathbot/file/17248525033221nkb98ht.jpg

The image contains two sets of linear equations. Let's start by solving the first set of linear equations using substitution:

### First System of Equations:
1. \( y = -6x - 7 \)
2. \( 4x - y = -3 \)

### Steps to Solve:

1. **Substitution Method**:
   - We already have \( y \) expressed in terms of \( x \) in equation 1: \( y = -6x - 7 \).
   - Substitute this expression for \( y \) in equation 2.

   Substitute \( y = -6x - 7 \) into \( 4x - y = -3 \):

   \[
   4x - (-6x - 7) = -3
   \]

   \[
   4x + 6x + 7 = -3
   \]

   \[
   10x + 7 = -3
   \]

2. **Solve for \( x \)**:
   
   \[
   10x = -3 - 7
   \]

   \[
   10x = -10
   \]

   \[
   x = -1
   \]

3. **Find \( y \) using \( x = -1 \) in equation 1**:

   \[
   y = -6(-1) - 7
   \]

   \[
   y = 6 - 7
   \]

   \[
   y = -1
   \]

### Solution:
The solution to the first system of equations is \( x = -1 \) and \( y = -1 \).

If you have any questions or want more details on the solution, please let me know! Here are five related questions for further practice:

1. How would the solution change if the first equation was \( y = -6x + 7 \)?
2. Can you solve the second system of equations using substitution?
3. What is the graphical representation of this system of equations?
4. How do you verify that the solution satisfies both equations?
5. How would you solve the system using the elimination method?

**Tip:** Always check your solution by substituting the values back into the original equations to ensure they satisfy both equations.

Learn how to solve a system of linear equations y = -6x - 7 and 4x - y = -3 using the substitution method. Detailed step-by-step solution provided. Suitable for Grades 8-10.

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