x-3y+7=2x+7y-5=6                                                                                                                                                                                                       x-3y+7=6                                                                                                                                                                                             2x+7y-5=6                                                                                                                                                                                  x-3y=_____                                                                                                                                                                        2x+7y=____

You have a system of equations to solve. Let's break it down step by step.

### Given:
1. \( x - 3y + 7 = 6 \)
2. \( 2x + 7y - 5 = 6 \)

### Simplifying each equation:

**Equation 1:**

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

Subtract 7 from both sides:

\[ x - 3y = 6 - 7 \]

\[ x - 3y = -1 \]

**Equation 2:**

\[ 2x + 7y - 5 = 6 \]

Add 5 to both sides:

\[ 2x + 7y = 6 + 5 \]

\[ 2x + 7y = 11 \]

### Summary:

- \( x - 3y = -1 \)
- \( 2x + 7y = 11 \)

Would you like to see how to solve for \( x \) and \( y \) using these equations?

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Here are 5 questions related to this problem:
1. How would you solve the system of equations using substitution?
2. What is the graphical interpretation of the system of equations?
3. How do you solve a system of equations using the elimination method?
4. What happens if the two lines in the system of equations are parallel?
5. Can you solve the system using matrices?

**Tip:** When solving systems of linear equations, always double-check your simplifications to avoid calculation errors.

Explore how to solve the system of equations x - 3y = -1 and 2x + 7y = 11 step-by-step. Learn the methods of substitution and elimination in solving linear equations. Suitable for high school students and anyone interested in algebraic problem-solving.

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