Solve the system by the method of your choice.
6 x equals y minus 2
6 x minus y equals 7


To solve the system of equations:

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

we can use the substitution method or the elimination method. Here, I will use the substitution method.

First, we solve the first equation for \( y \):

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

Next, we substitute this expression for \( y \) into the second equation:

\[ 6x - (6x + 2) = 7 \]

Simplify the equation:

\[ 6x - 6x - 2 = 7 \]
\[ -2 = 7 \]

This is a contradiction, which means that there is no solution to this system of equations. The lines represented by these equations are parallel and never intersect.

### Conclusion:
The system of equations has no solution because the lines are parallel.

Would you like details or have any questions? Here are 5 more questions you can ask:

1. How do you solve a system of equations using the elimination method?
2. Can you graphically demonstrate why the system has no solution?
3. How can you tell if a system of equations is inconsistent?
4. What are some real-world applications of solving systems of equations?
5. Can you explain the differences between consistent, inconsistent, and dependent systems?

**Tip:** When dealing with systems of equations, always check if the lines are parallel, intersecting, or coinciding to determine the nature of the solutions.

Learn how to solve the system of equations 6x = y - 2 and 6x - y = 7 using the substitution method. Understand why the system has no solution due to the parallel nature of the lines represented by these equations. Suitable for high school students.

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