The system of equations given is:

1) y = x + 4
2) 2x - 2y = 2

First, let's simplify the second equation by dividing every term by 2:

x - y = 1

Now, we can rewrite this equation in terms of y:

y = x - 1

Now we have two equations:

1) y = x + 4
2) y = x - 1

These two lines have the same slope (1), but different y-intercepts (+4 and -1). Therefore, they are parallel and will never intersect.

This means the system of equations is inconsistent (no solution exists that satisfies both equations simultaneously).

Since there is no solution, the system is also independent (one equation cannot be derived from the other).

Question

The system of equations given is:

1) y = x + 4
2) 2x - 2y = 2

First, let's simplify the second equation by dividing every term by 2:

x - y = 1

Now, we can rewrite this equation in terms of y:

y = x - 1

Now we have two equations:

1) y = x + 4
2) y = x - 1

These two lines have the same slope (1), but different y-intercepts (+4 and -1). Therefore, they are parallel and will never intersect.

This means the system of equations is inconsistent (no solution exists that satisfies both equations simultaneously).

Since there is no solution, the system is also independent (one equation cannot be derived from the other).

Knowee AI · Accepted Answer