Identify the type of system of equations and solve the system of equations if possible.2𝑥−6𝑦=44𝑥−6𝑦=8Select the type of system and most correct meaning below.Group of answer choicesAn independent system; the lines will cross in only one place so there is only one solution.An inconsistent system; the parallel lines will never cross so there is no solution.A dependent system; there is really only one line so any of the infinite number of points on that line is a solution.An inconsistent system; there is really only one line so any of the infinite number of points on that line is a solution.A dependent system; the parallel lines will never cross so there is no solution

The given system of equations is:

2x - 6y = 4 4x - 6y = 8

First, let's simplify these equations by dividing the first equation by 2 and the second equation by 4:

x - 3y = 2 x - 1.5y = 2

Now, it's clear that these two equations are not the same and they are not multiples of each other. Therefore, they represent two different lines. However, if we look at the coefficients of x and y in both equations, we can see that the coefficient of x is the same in both equations, but the coefficients of y are different. This means that the lines represented by these equations have the same slope but different y-intercepts, which means they are parallel to each other.

Parallel lines never intersect, so there is no point (x, y) that satisfies both equations at the same time. Therefore, this system of equations has no solution.

So, the correct answer is: An inconsistent system; the parallel lines will never cross so there is no solution.