To determine whether the system of equations is consistent or inconsistent, and whether it has one solution, no solution, or infinitely many solutions, we can analyze the given equations.
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The first equation is: \[ 3y = -6x + 12 \] We can rewrite it in slope-intercept form (y = mx + b): \[ y = -2x + 4 \]
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The second equation is: \[ 2x + y = 8 \] We can also rewrite it in slope-intercept form: \[ y = -2x + 8 \]
Now we have:
- The first line: \( y = -2x + 4 \)
- The second line: \( y = -2x + 8 \)
Both equations have the same slope of -2, indicating they are parallel lines. However, they have different y-intercepts (4 and 8), which means they will never intersect.
Since the two lines are parallel and do not meet at any point, the system has no solutions and is considered inconsistent.
Therefore, the correct statement about the system is: The system is inconsistent because it has no solution.