How many solutions does the system of equations have?
y = 6x + 2 and 3y – 18x = 12
To find out the number of solutions, we need to analyze the system of equations.
First, let's rewrite the second equation in terms of y:
3y - 18x = 12
3y = 18x + 12
y = 6x + 4
Comparing this new equation with the first equation (y = 6x + 2), we can see that they have the same slope (6) but different y-intercepts (2 and 4).
Since the slopes are equal, the lines are parallel. However, since the y-intercepts are different, the lines do not intersect.
Therefore, the system of equations has no solution.