We have the system of equations:
12x - 9y = 27
8x - 6y = 18
If we are going to solve the equation by graphing, we need to put these equations in the slope-intercept form:
y = m*x + b
Where m is the slope of the equation, and b is the intercept of the graph with the vertical line. For the first equation:
12x - 27 = 9y
Dividing by 9:
12x/9 - 27/9 = y
=> y = 4x/3 - 3 ...(1)
Now, for the second equation:
8x - 18 = 6y
Dividing by 6:
y = 4x/3 - 3 ...(2)
We can see that (1) and (2) are identical, so we conclude that the system of equations is consistent dependent (there are infinite solutions).