How many solutions does the system of equations have?
y = 6x + 2 and 3y - 18x = 12
To find the number of solutions in a system of equations, we need to determine if the lines represented by the equations are parallel, coincident, or intersecting.
The given system of equations can be written in the form:
Equation 1: y = 6x + 2
Equation 2: -18x + 3y = 12
To simplify equation 2, we can rewrite it as:
-18x + 3y = 12
3y = 18x + 12
y = 6x + 4
Comparing Equation 1 and Equation 2, we can see that both equations are in the form y = mx + b, where m is the slope.
The equation y = 6x + 2 has a slope of 6, and the equation y = 6x + 4 has a slope of 6 as well. The slopes are equal, indicating that the two lines are parallel.
Parallel lines do not intersect, meaning there are no common solutions for the system of equations.
Therefore, the system of equations has no solutions.