System of Inequatilies

Today, we learned how to solve the system of inequalities and graph the solution of inequality. To sketch the graph of an inequality, begin by sketching the graph of the corresponding equation (which is replace the inequality sign with the equal sign). The graph of the equation will normally seperate the plane into two or more regions. In each such region, one of the following must be true.

1 All points in the region are solutions of the inequality

2 No point in the region is a solution of the inequality

Note: During the graph, we use a dashed line for < or >，and a solid line for ≤ or ≥.

Example： x+y≤5

                  x≥2

                  y≥0

                             

Replace the inequality sign with the equal sign, and sketch the graph of the resulting equation with solid line since all inequality are ≤ or ≥. Then test one point in each of the regions formed by graph to find their solution, and the shadow in red will be the final solution.