Question

Which graph represents the solution set for the system 2x + y ≤ 3 and y − x > 2?

Answer 1

You can identify the lines and their colour either by
1. the y-intercepts.  
First equation has a y-intercept of 3 and second has a y-intercept of 2.
So first equation is blue, and second is red.
2. the slopes
First equation has a negative slope (so blue), and second has a positive slope (so red).

Now work on each of the equations.
1. first equation (blue)
If we put x=0, we end up with the equation y≤3, the ≤ sign indicates that the region is BELOW the BLUE line.
2. second equation (red).
If we put x=0, we end up with the equation y>2, the > sign indicates that the region is ABOVE the RED line AND the red line should be dotted (full line if ≥).

So at the point, it won't be too hard to find the correct region.

To confirm, take a point definitely in the region, such as (-6,0) and substitute in each equation to make sure that both conditions are satisfied.