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To determine whether the system of equations has one solution, infinite solutions, or no solutions, we can analyze the two equations:
1. \( x - 2y = 6 \)
2. \( 3x - 6y = 18 \)
We can simplify the second equation. Notice that the second equation can be expressed as:
\[
3(x - 2y) = 18
\]
Dividing both sides by 3 gives us:
\[
x - 2y = 6
\]
Now we see that both equations are actually the same:
1. \( x - 2y = 6 \)
2. \( x - 2y = 6 \)
Since both equations represent the same line in a coordinate plane, they have infinitely many solutions as every point on this line satisfies both equations.
Thus, the system of equations has **infinite solutions**.