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Algebra 2 Notes Section 3.1: Solve Linear Systems by Graphing Objective(s): Vocabulary: I. System of Two Linear Equations: (See Glossary p. 1080) II. Solution of a System: III. Consistent: IV. Inconsistent: V. Independent: VI. Dependent: Examples: 1. Graph the linear system and estimate the solution. Then check the solution algebraically. 5x – 2y = -10 2x – 4y = 12 2. Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 6x – 2y = 8 3x – y = 4 Notes 3.1 page 2 3. Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. -4x + y = 5 -4x + y = -2 4. A soccer league offers two options for membership plans. Option A includes an initial fee of $40 and costs $5 for each game played. Option B costs $10 for each game played. After how many games will the total cost of the two options be the same? Algebra 2 Notes Section 3.2: Solve Linear Systems Algebraically Objective(s): Vocabulary: I. Substitution Method: Step 1: Step 2: Step 3: *NOTE: Choose your variable in Step 1 wisely to make your work easier! II. Elimination Method: Step 1: Step 2: Step 3: Examples: 1. Solve the system using the substitution method. 3x + 2y = 1 -2x + y = 4 2. Solve the system using the elimination method. 8x + 2y = 4 -2x + 3y = 13 Notes 3.2 page 2 3. Solve the linear system using any algebraic method. a) 2x - 3y = 4 6x - 9y = 8 c) 8x + 9y = 15 5x – 2y = 17 b) x–y=4 -6x + 6y = -24 d) 3x – 6y = 9 -4x + 7y = -16 4. At a pizza restaurant it costs $4 to make a small pizza that sells for $12, and it costs $6 to make a large pizza that sells for $15. In one week, the restaurant spent a total of $1100 making pizzas and sold all of them for $2910. how many small pizzas were sold? Algebra 2 Notes Section 3.3: Graph Systems of Linear Inequalities Objective(s): Vocabulary: I. System of Linear Inequalities: (See Glossary p. 1079) II. Solution of a System of Inequalities: III. Graph of a System of Inequalities: III. Graphing a System of Linear Inequalities: Step 1: Step 2: *NOTE: You may want to use colored pencils to distinguish the different half-planes. Examples: 1. Graph the system of inequalities. a) y < 3x + 2 y > -x + 4 b) 4x + 2y > 8 y < -2x - 3 Notes 3.3 page 2 2. Graph the system of inequalities. a) y< 2 y > |x – 1| b) x > 10 x < 70 y>x y 4 x 30 7 100 90 80 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80 90 100 Algebra 2 Notes Section 3.4: Solve Systems of Linear Equations in Three Variables Objective(s): Vocabulary: I. Linear Equation in Three Variables: II. System of Three Linear Equations: (See Glossary p. 1079) III. Solution of a System of Three Linear Equations: I. Ordered Triple: IV. Elimination Method for a Three-Variable System: Step 1: Step 2: Step 3: Note: If you obtain a false equation, such as 0 = 1, in any of the steps, then the system has . If you do not obtain a false equation, but obtain an identity such as 0 = 0, then the system has Examples: 1. Solve the system. 2x – y + 6z = -4 6x + 4y – 5z = -7 -4x – 2y + 5z = 9 . Notes 3.4 page 2 2. Solve the system. a) x+y–z=2 3x + 3y – 3z = 8 2x – y + 4z = 7 b) x+y+z=6 x–y+z=6 4x + y + 4z = 24 c) 3x + y – 2z = 10 6x – 2y + z = -2 x + 4y + 3z = 7 4. At a carry-out pizza restaurant, an order of 3 slices of pizza, 4 breadsticks, and 2 sodas costs $13.35. A second order of 5 slices of pizza, 2 breadsticks, and 3 sodas costs $19.50. If four breadsticks and a soda cost $.30 more than a slice of pizza, what is the cost of each item?