whether the system of equations is consistent or inconsistent and if it is independent or dependent. y=2x−3𝑦=2𝑥-3 2x−2y=2

To determine whether the system of equations is consistent or inconsistent and if it is independent or dependent, we need to analyze the equations. The given system of equations is:

1. y = 2x - 3
2. 2x - 2y = 2

First, let's simplify the second equation by dividing all terms by 2:

x - y = 1

Now, let's express this equation in terms of y:

y = x - 1

Now, we have two equations:

1. y = 2x - 3
2. y = x - 1

These two equations represent two lines in a plane. If the lines intersect at a single point, the system is consistent and independent. If the lines coincide (i.e., they are the same line), the system is consistent and dependent. If the lines are parallel and do not intersect, the system is inconsistent.

In this case, the lines represented by the equations y = 2x - 3 and y = x - 1 have different slopes (2 and 1, respectively), so they are not the same line and they are not parallel. Therefore, they must intersect at a single point.

So, the system of equations is consistent and independent.