The system of equations is consistent and dependent.
However, the two equations you provided are not consistent with this graph.
The equation 2y=2x+2 simplifies to y=x+1, which is the same as the equation of the graph.
Therefore, the system of equations is consistent and dependent.
This means that the lines represented by the two equations coincide, and there are infinitely many solutions to the system.
Here is a breakdown of the process:
Identify the slope and y-intercept of the graph:
From the graph, we can see that the line has a slope of 1 and a y-intercept of 1.
Convert the equations to slope-intercept form: The equation y=x+1 is already in slope-intercept form.
The equation 2y=2x+2 can be converted to slope-intercept form by dividing both sides by 2: y=x+1.
Compare the equations: Since both equations have the same slope and y-intercept, they represent the same line.
Therefore, the system of equations is consistent and dependent.