y=
2x−7
minus, 6, x, plus, 7, y, equals, 15
−6x+7y=
15

You have the following system of equations:

1. \( y = 2x - 7 \)
2. \( -6x + 7y = 15 \)

We can solve this system using substitution or elimination. I'll use **substitution** since the first equation already expresses \( y \) in terms of \( x \).

### Step-by-step solution:

1. From the first equation, \( y = 2x - 7 \), substitute \( y \) into the second equation:
   \[
   -6x + 7(2x - 7) = 15
   \]

2. Simplify the second equation:
   \[
   -6x + 14x - 49 = 15
   \]
   \[
   8x - 49 = 15
   \]

3. Solve for \( x \):
   \[
   8x = 15 + 49
   \]
   \[
   8x = 64
   \]
   \[
   x = 8
   \]

4. Now, substitute \( x = 8 \) back into the first equation to solve for \( y \):
   \[
   y = 2(8) - 7
   \]
   \[
   y = 16 - 7
   \]
   \[
   y = 9
   \]

### Final solution:
- \( x = 8 \)
- \( y = 9 \)

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

Here are 5 questions to expand your understanding:
1. How would you solve this system using the elimination method?
2. What happens if both equations represent the same line?
3. Can you graph both equations to verify the solution?
4. What is the general process for solving systems of equations with substitution?
5. How can we check the solution by plugging \( x \) and \( y \) back into both equations?

**Tip:** Always substitute your solution back into the original equations to verify correctness.

Discover how to solve the system of equations y = 2x - 7 and -6x + 7y = 15 using the substitution method. Follow the step-by-step guide to solve for x and y, perfect for students in Grades 8-10 learning about algebra and systems of equations.

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