We are solving the system of linear equations:

1. $y = 3x - 6$
2. $-3x + y = 6$

Step 1: Substitution

From the first equation, we already have $y = 3x - 6$. Substitute this into the second equation:

$-3x + (3x - 6) = 6$

Simplify: $-3x + 3x - 6 = 6$

$0 - 6 = 6$

$-6 = 6$

Step 2: Analyze the Result

The equation $-6 = 6$ is a contradiction, meaning there is no solution to this system of equations. The two lines are parallel and never intersect.

Final Answer

The system of equations is inconsistent (no solution).

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Do you want further clarification or have any questions? Here are 5 related questions to consider:

1. How do we determine if lines are parallel using their slopes?
2. What does it mean for a system of equations to have no solution geometrically?
3. How can we check for consistency in a system of equations?
4. Can you give another example of an inconsistent system?
5. How do we graph these two lines to visualize the result?

Tip: For systems of equations, comparing slopes is a quick way to check if the lines are parallel ($m_1 = m_2$).