6.5 S OLVING L INEAR I NEQUALITIES 6.6 S OLVING S YSTEMS OF I NEQUALITIES.

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6.5 S OLVING L INEAR I NEQUALITIES 6.6 S OLVING S YSTEMS OF I NEQUALITIES

Graph the solutions of the linear inequality. Example 2A: Graphing Linear Inequalities in Two Variables y  2 x – 3 Check

Graphing Linear Inequalities Step 1 Solve the inequality for y (slope-intercept form). Step 2 Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for. Step 3 Shade the half-plane above the line for y > or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer.

Graph the solutions of the linear inequality. Example 2B: Graphing Linear Inequalities in Two Variables 5 x + 2 y > –8

Graph the solutions of the linear inequality. Example 2C: Graphing Linear Inequalities in two Variables 4 x – y + 2 ≤ 0

Ada has at most 285 beads to make jewelry. A necklace requires 40 beads, and a bracelet requires 15 beads. Example 3a: Application Write a linear inequality to describe the situation and then graph. Give two combinations of necklaces and bracelets that Ada could make.

Write an inequality to represent the graph. Example 4A: Writing an Inequality from a Graph

Example 2A: Solving a System of Linear Inequalities by Graphing Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions. y ≤ 3 y > –x + 5 6.6 S OLVING S YSTEM OF I NEQUALITIES

Example 2B: Solving a System of Linear Inequalities by Graphing Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions. –3x + 2y ≥ 2 y < 4x + 3

In Lesson 6-4, you saw that in systems of linear equations, if the lines are parallel, there are no solutions. With systems of linear inequalities, that is not always true.

Graph the system of linear inequalities. Example 3A: Graphing Systems with Parallel Boundary Lines y ≤ –2x – 4 y > –2x + 5 This system has no solutions. In Lesson 6-4, you saw that in systems of linear equations, if the lines are parallel, there are no solutions. With systems of linear inequalities, that is not always true.

Graph the system of linear inequalities. Example 3B: Graphing Systems with Parallel Boundary Lines y > 3x – 2 y < 3x + 6 The solutions are all points between the parallel lines but not on the dashed lines.

Example 4: Application In one week, Ed can mow at most 9 times and rake at most 7 times. He charges \$20 for mowing and \$10 for raking. He needs to make more than \$125 in one week. Show and describe all the possible combinations of mowing and raking that Ed can do to meet his goal. List two possible combinations. Solutions

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