x - 2y = 6
3x - 6y = 18
one solution, no solution, infinite
The two equations can be simplified by dividing the first equation by 2:
x - 2y = 6 becomes 1/2x - y = 3
Now we can compare the simplified equation with the second equation:
1/2x - y = 3
3x - 6y = 18
We can see that the coefficients of x and y are proportional, which means the two equations represent the same line. Therefore, the system has infinitely many solutions.