1. Graph of inequality in two variables Solution of an inequality in two variables is the set of all points that satisfy the inequality. 1) Replace the inequality symbol by “=“ and graph. a)Solid line if b)Dashed line if 2)Pick a test point (usually (0,0)) and test in the inequality. If false, shade half-plane not containing the point If true, shade half-plane that does contain the point Solution of an inequality in two variables is the set of all points that satisfy the inequality. 1) Replace the inequality symbol by “=“ and graph. a)Solid line if b)Dashed line if 2)Pick a test point (usually (0,0)) and test in the inequality. If false, shade half-plane not containing the point If true, shade half-plane that does contain the point 10.7 Systems of Inequalities
2. Graph a non-linear inequality a)
2. Graph a non-linear inequality b)
3. Graph a linear inequality c)
3. Graph a horizontal or vertical line a) b) c) d) a) b) c) d)
3. Graph without using a test point to determine shaded region In some cases, easier to graph when y is isolated to one side of the inequality. Example In some cases, easier to graph when y is isolated to one side of the inequality. Example
4. Graph a system of inequalities Graph the system 1) Graph the system 1)
4. Graph a system of inequalities Graph the system 2) Graph the system 2)
5. Determine the vertices of a bounded region Graph the region bounded by the system and determine the vertices (corner points) 1) Graph the region bounded by the system and determine the vertices (corner points) 1)
5. Determine the vertices of a bounded region Graph the region and determine the vertices (corner points) 2) Graph the region and determine the vertices (corner points) 2)
6. Unbounded System Some systems may be unbounded or have no solution. 1) Some systems may be unbounded or have no solution. 1) A region is bounded if we can find a large enough circle to contain the region.
6. more practice 2) 2) A region between parallel lines.
7. Write a system from the given graph (3,0) (1,3) (1,-3)(5,-3)