The graph of a system of inequalities is a visual representation of the solutions to the equation. It is used to show the area of the solution set as well as the range of possible solutions. The graph is usually created by plotting the lines of the inequalities on a coordinate plane. Knowing which graph shows the solution to a system of inequalities can be beneficial in solving the system.
Different Types of Graphs
There are three different types of graphs that can be used to show the solution to a system of inequalities: a line graph, a circle-and-dashes graph, and a shaded graph. Each graph has its own advantages and disadvantages.Line Graph
The line graph shows the solution to the system of inequalities by plotting the lines of the inequalites on a coordinate plane. The line graph is beneficial because it is easy to read and understand. However, the line graph does not show the range of possible solutions.Circle-and-Dashes Graph
The circle-and-dashes graph shows the solution to the system of inequalities by plotting the lines of the inequalites on a coordinate plane and then drawing circles and dashes around the points where the lines intersect. The advantage of the circle-and-dashes graph is that it shows the range of possible solutions. The disadvantage is that it is more difficult to read than the line graph.Shaded Graph
The shaded graph shows the solution to the system of inequalities by shading the area of the solution set on a coordinate plane. The advantage of the shaded graph is that it is easier to read than the circle-and-dashes graph. The disadvantage is that it does not show the range of possible solutions.Comparison
| Graph | Advantage | Disadvantage |
|---|---|---|
| Line Graph | Easy to read and understand | Does not show the range of possible solutions |
| Circle-and-Dashes Graph | Shows the range of possible solutions | More difficult to read than the line graph |
| Shaded Graph | Easier to read than the circle-and-dashes graph | Does not show the range of possible solutions |