x - 2y = 6

3x - 6y = 18

does this have one solution or no solutions or infinite solutions

1 answer

To determine the number of solutions to the system of equations, we can convert the equations to slope-intercept form (y = mx + b).

Starting with the first equation:
x - 2y = 6
Rearranging, we get:
-2y = -x + 6
Dividing by -2:
y = 1/2x - 3

Now, let's work on the second equation:
3x - 6y = 18
Rearranging, we get:
-6y = -3x + 18
Dividing by -6:
y = 1/2x - 3

As we can observe, both equations have the same slope (1/2) and the same y-intercept (-3). This means that the two lines are parallel and will never intersect. Therefore, the system of equations has no solution.