Solving Systems of Linear Inequalities Graphically

Let's plot the given points on the same coordinate plane as the system of inequalities.

When looking at the four points, the first thing we can notice is that $(0,\text{-}4)$ and $(\text{-}1,\text{-}6)$ lie squarely within the solution set, and the points $(1,\text{-}2)$ and $(2,\text{-}4)$ rest on the boundary lines. What does it mean when a line is dashed and when it is solid?

• A solid line tells us that the inequality is not strict. Therefore, the points on the boundary line are solutions to the inequality.
• A dashed line tells us that the inequality is strict. Therefore, the points on the boundary line are not solutions to the inequality.

With the above in mind, we can conclude that $(2,\text{-}4)$ is a solution to the system because it lies on a solid line. However, the point $(1,\text{-}2),$ which lies on both a solid and a dashed line, is a solution to one of the inequalities but not a solution to the other. Therefore, $(1,\text{-}2)$ does not belong with the others as it is not a solution.