Extension

To determine how many solutions there are for the system of equations given by:

1. \( 3y = 3x + 6 \)
2. \( y = x + 2 \)

we can first simplify the first equation:

1. Divide both sides of the first equation by 3:

\[ y = x + 2 \]

Now we have both equations in the same form:

1. \( y = x + 2 \)
2. \( y = x + 2 \)

Since both equations are identical, they represent the same line. Therefore, every point on this line is a solution to the system of equations.

This means there are infinitely many solutions to this system of equations since they are the same line.