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Algebra 2 Warm-up (Quiz Review)

Algebra 2 Warm-up (Quiz Review). 1. Solve using Substitution. 2. Solve using elimination. 3. Solve by Graphing. Warm-up: Answers. 1. Solve using Substitution. (-1, 5) 2. Solve using elimination. (0, -2) 3. Solve by Graphing (-3, 1). Check Homework.

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Algebra 2 Warm-up (Quiz Review)

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  1. Algebra 2 Warm-up(Quiz Review) 1. Solve using Substitution. 2. Solve using elimination. 3. Solve by Graphing

  2. Warm-up: Answers 1. Solve using Substitution. (-1, 5) 2. Solve using elimination. (0, -2) 3. Solve by Graphing (-3, 1)

  3. Check Homework • P. 167 [Quiz for lessons 3.1-3.2] Take Quiz 3.1-3.2

  4. Section 3.3 Objective: Graph systems of linear inequalities. • Graph paper (fold into ¼’s) • Colored pencils • Powerpoint 3.3

  5. Just discuss • (Graph each of the following)

  6. Solving Systems of Linear Inequalities The graph of a linear inequality in two variables is a half-plane. The boundary line of the half-plane is dashed if the inequality is < or > and solid if the inequality is £or ³. Two or more linear inequalities form a system of linear inequalities or simply a system of inequalities. A solution of a system of a system of linear inequalities is an ordered pair that is a solution of each inequality in the system. The graph of a system of linear inequalities is the graph of all solutions of the system.

  7. EX 1 y < 2x – 2 y > –2/3 x + 2 m = 2/1 b = –2m = -2/3 b = 2

  8. EX 2 Solve the system by graphing: x ≤ 3y < –1y < x – 2x ≥ 0 This purple region is the solution to the system.

  9. A Triangular Solution Region y < 2 Inequality 1 x³ –1 Inequality 2 y> x – 2 Inequality 3 CHECK Ex 3 Graph the system of linear inequalities. SOLUTION Graph all three inequalities in the same coordinate plane. The graph of the system is the overlap, or the intersection, of the three half-planes shown. You can see from the graph that the point (2, 1) is a solution of the system. To check this, substitute the point into each inequality. 1 < 2 True. 2³ –1 True. True. 1 > 2 – 2

  10. A Triangular Solution Region y < 2 Inequality 1 x³ –1 Inequality 2 y> x – 2 Inequality 3 Graph the system of linear inequalities. The point (0, 3) is not in the graph of the system. Notice (0, 3) is not a solution of inequality 1. This point is not a solution of the system. When graphing a system of inequalities, it is helpful to find each corner point (or vertex). For instance, this graph has three corner points:(–1, 2), (–1, –3), and (4, 2).

  11. Assignments Homework: p. 171 # 3, 7, 13, 21, 23 [on graph paper]

  12. Closure Balloons cost $1.50 and Crepe paper costs $0.85. You are in charge of decorating for the homecoming dance. You purchase ten bags of balloons and six rolls of crepe paper for $20.10. You soon realize that this is not enough to decorate the entire gym. On your second trip, you spend $12.80 on four bags of balloons and eight rolls of crepe paper. What was the price of each item?

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