The solutions to the individual inequalities should not overlap.
Example Solution: y>x+2 y
Practice makes perfect
For the solution of a system to have no solution, it must be true that the individual solution sets do not have any values in common. This means the shaded region of each inequality should extend in different directions. Let's write the inequalities so that the boundary lines are parallel.
y=x+2 & (I) y=x-2 & (II)
Let's look at the graphs of these boundary lines.
From the graph above, we can see that we need to shade above Inequality (I) and below Inequality (II) to ensure the individual solution sets do not overlap. By considering this, let's write our system.
y>x+2 & (I) y
By the way — we should acknowledge that there are infinitely many solutions to this exercise.
