How many solutions does the system of equations have?
y = 6x + 2 and 3y - 18x = 12
(1 point)
A-one
B-two
C-infinitely many
D-none
To find the number of solutions, we can first determine if the system of equations is consistent (meaning it has at least one solution) and then see how many solutions it has.
Let's rearrange the second equation to slope-intercept form:
3y - 18x = 12
3y = 18x + 12
y = 6x + 4
Comparing the two equations, we see that they have the same slope (6) but different y-intercepts (2 and 4).
Since the slopes are equal but the y-intercepts are different, the lines represented by these equations are parallel and will never intersect. Therefore, the system of equations has no solutions.
The answer is D) none.