Answer:
To graph a system of linear inequalities, you will need to graph each inequality separately on the same set of axes. Here is the general process for graphing a linear inequality:
Begin by plotting the inequality's equation in standard form: Ax + By > C (or < C, or = C).
Determine the values of x and y that make the inequality true. To do this, set each side of the inequality equal to zero and solve for x and y. For example, if the inequality is 2x + 3y > 6, you would set 2x + 3y = 0 and solve for x and y.
Graph the line that represents the equation.
Determine the direction of the inequality by looking at the inequality symbol. If the symbol is ">," the line will be shaded above it. If the symbol is "<," the line will be shaded below it. If the symbol is "≥," the line will be shaded above it, including the line itself. If the symbol is "≤," the line will be shaded below it, including the line itself.
Repeat the process for each additional inequality in the system.
The solution to the system of inequalities is the area where all of the shaded regions overlap. This is the region where all of the inequalities are simultaneously true.
Here is an example of how to graph a system of linear inequalities:
Suppose we want to graph the following system of inequalities:
2x + 3y > 6
-x + 2y < 4
To graph the first inequality, we set 2x + 3y = 0 and solve for x and y. This gives us x = -(3/2)y. We can then plot this line on a graph.
Next, we determine the direction of the inequality by looking at the inequality symbol. In this case, the symbol is ">," so we shade the area above the line.
To graph the second inequality, we set -x + 2y = 0 and solve for x and y. This gives us x = (1/2)y. We can then plot this line on the same graph.
Next, we determine the direction of the inequality by looking at the inequality symbol. In this case, the symbol is "<," so we shade the area below the line.
The solution to the system of inequalities is the area where the shaded regions overlap. This is the region where both inequalities are simultaneously true.