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**Linear System of Equations**

Classify Systems Independent Dependent Inconsistent Methods for Solving Tables Graphing Substitution Elimination Matrices π¦=π₯+3 π₯+π¦=1 (β1, 2) π+(π+π)=π ππ=βπ π=βπ π= βπ +π=π βπ+π=π π+π=π ππ=π π=π π=π+π βπ=π π₯ π¦=π₯+3 π₯+π¦=1 β2 1 3 β1 2 βπ π π π | π π π π π π βπ π

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**Linear System of Inequalities**

Maximize: 3π₯+2π¦ βπ+ππβ€π π+π<π πβ₯π πβ₯π (2, 1) =8 (2, 2) =10 (4, 4) =20 (7, 1) =23 Pg. 187 #1 β 13

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**Linear Systems 10 20 30 40 50 Classifying Systems**

Solving 2 Variable Systems Solving 3 Variable Systems Inequalities Modeling (Application) 10 20 30 40 50

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**Without graphing, classify each system**

Without graphing, classify each system. (independent, dependent, inconsistent) 5π₯+3π¦=9 π¦=β 3 5 π₯+3 Answer

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**Without graphing, classify each system**

Without graphing, classify each system. (independent, dependent, inconsistent) 5π₯+3π¦=9 3π¦=β5π₯+9 π¦=β 5 3 π₯+3 5π₯+3π¦=9 π¦=β 3 5 π₯+3 Independent

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**Without graphing, classify each system**

Without graphing, classify each system. (independent, dependent, inconsistent) 12π₯β4π¦=20 π¦=3π₯+3 Answer

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**Without graphing, classify each system**

Without graphing, classify each system. (independent, dependent, inconsistent) 12π₯β4π¦=20 β4π¦=β12π₯+20 π¦=3π₯β5 12π₯β4π¦=20 π¦=3π₯+3 Inconsistent

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**Without graphing, classify each system**

Without graphing, classify each system. (independent, dependent, inconsistent) 2π₯+6π¦=12 π¦=β 1 3 π₯+2 Answer

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**Without graphing, classify each system**

Without graphing, classify each system. (independent, dependent, inconsistent) 2π₯+6π¦=12 π¦=β 1 3 π₯+2 2π₯+6π¦=12 6π¦=β2π₯+12 π¦=β 1 3 π₯+2 Dependent

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**Without graphing, classify each system**

Without graphing, classify each system. (independent, dependent, inconsistent) β12π₯+2π¦=β15 18π₯β3π¦=27 Answer

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**Without graphing, classify each system**

Without graphing, classify each system. (independent, dependent, inconsistent) β12π₯+2π¦=β15 18π₯β3π¦=27 β12π₯+2π¦=β15 2π¦=12π₯β15 π¦=6π₯β 15 2 18π₯β3π¦=27 β3π¦=β18π₯+27 π¦=6π₯β9 Inconsistent

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**Without graphing, classify each system**

Without graphing, classify each system. (independent, dependent, inconsistent) 15π₯+6π¦=6 10π₯+4π¦=4 Answer

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**Without graphing, classify each system**

Without graphing, classify each system. (independent, dependent, inconsistent) 15π₯+6π¦=6 10π₯+4π¦=4 15π₯+6π¦=6 6π¦=β15π₯+6 π¦=β 5 2 π₯+1 10π₯+4π¦=4 4π¦=β10π₯+4 π¦=β 5 2 π₯+1 Dependent

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**Solve the system by: Graphing**

π¦=2π₯β4 π₯β4π¦=β3 Answer

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**Solve the system by: Graphing**

π¦=2π₯β4 π₯β4π¦=β12 (4, 4)

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**Solve the system by: Substitution**

β2π₯βπ¦=β9 π¦=β5π₯+15 Answer

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**Solve the system by: Substitution**

β2π₯βπ¦=β9 π¦=β5π₯+15 β2π₯βπ¦=β9 β2π₯β(β5π₯+15)=β9 β2π₯+5π₯β15=β9 3π₯=6 π₯=2 π¦=β5π₯+15 π¦=β π¦=5 (2, 5)

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**Solve the system by: Elimination**

β8π₯β7π¦=β28 5π₯+6π¦=24 Answer

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**Solve the system by: Elimination**

β8π₯β7π¦=β28 5π₯+6π¦=24 π β8π₯β7π¦=β28 π(5π₯+6π¦=24) β48π₯β42π¦=β168 35π₯+42π¦=168 β13π₯=0 π₯=0 5π₯+6π¦=24 5 0 +6π¦=24 6π¦=24 π¦=4 (0, 4)

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**Solve the system by: Your Choice**

6π¦+11+π₯=0 8π₯=β4β6π¦ Answer

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**Solve the system by: Your Choice**

6π¦+11+π₯=0 8π₯=β4β6π¦ π₯+6π¦=β11 β8π₯β6π¦=4 β7π₯=β7 π₯=1 6π¦+11+π₯=0 6π¦ =0 6π¦=β12 π¦=β2 (1, β2)

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**Solve the system by: Your Choice**

β4π¦=8π₯+12 0=18π¦+12π₯β90 Answer

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**Solve the system by: Your Choice**

β4π¦=8π₯+12 0=18π¦+12π₯β90 0=18π¦+12π₯β90 0=18 β2π₯β3 +12π₯β90 0=β36π₯β54+12π₯β90 144=β24π₯ β6=π₯ β4π¦=8π₯+12 π¦=β2π₯β3 π¦=β2 β6 β3 π¦=9 (β6, 9)

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**Write a matrix to represent the system.**

6π₯+2π¦+π§=30 β3π₯+3π§=0 β2π₯+5π¦+4π§=3 Answer

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**Write a matrix to represent the system.**

6π₯+2π¦+π§=30 β3π₯+3π§=0 β2π₯+5π¦+4π§=3 6 2 1 β3 0 3 β

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**What system is represented by the matrix:**

β Answer

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**What system is represented by the matrix:**

β 2π₯+7π¦+π§=9 3π₯β2π¦=6 π₯+2π¦+π§=0

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**Solve the system by: Your Choice**

6π₯β5π§=β11 π₯βπ¦=β12 β4π₯β4π¦+5π§=β25 Answer

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**Solve the system by: Your Choice**

6π₯β5π§=β11 π₯βπ¦=β12 β4π₯β4π¦+5π§=β25 π₯βπ¦=β12 π₯β6=β12 π₯=β6 2π₯β4π¦=β36 βπ(π₯βπ¦=β12) β2π₯+2π¦=24 β2π¦=β12 π¦=6 6π₯β5π§=β11 β4π₯β4π¦+5π§=β25 2π₯β4π¦=β36 6π₯β5π§=β11 6 β6 β5π§=β11 β36β5π§=β11 β5π§=25 π§=β5 6 0 β5 1 β1 0 β4 β β11 β12 β25 (β6, 6, β5)

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**Solve the system by: Your Choice**

6π₯β5π¦+π§=β17 2π₯βπ¦+π§=β5 π§=β3π₯β8 Answer

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**Solve the system by: Your Choice**

6π₯β5π¦+π§=β17 2π₯βπ¦+π§=β5 π§=β3π₯β8 6π₯β5π¦+ β3π₯β8 =β17 3π₯β5π¦=β9 2π₯βπ¦+ β3π₯β8 =β5 βπ₯βπ¦=3 βπ₯βπ¦=3 βπ₯β(0)=3 βπ₯=3 π₯=3 3π₯β5π¦=β9 π(βπ₯βπ¦=3) β3π₯β3π¦=9 β8π¦=0 π¦=0 6 β5 1 2 β β17 β5 β8 π§=β3π₯β8 π§=β3 3 β8 π§=1 (3, 0, 1)

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**Solve the system by: Your Choice**

π₯+6π¦β2π§=25 π₯β5π¦β3π§=9 6π₯+π¦+6π§=β28 Answer

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**Solve the system π₯+6π¦β2π§=25 βπ(π₯β5π¦β3π§=9) βπ₯+5π¦+3π§=β9 11π¦+π§=16**

6π₯+π¦+6π§=β28 βπ(π₯β5π¦β3π§=9) β6π₯+30π¦+18π§=β54 31π¦+24π§=β82 π₯+6π¦β2π§=25 π₯β5π¦β3π§=9 6π₯+π¦+6π§=β28 31π¦+24π§=β82 βππ(11π¦+π§=16) β264π¦β24π§=β384 β233π¦=β466 π¦=2 11π¦+π§=16 11 2 +π§=16 22+π§=16 π§=β6 π₯β5π¦β3π§=9 π₯β5 2 β3 β6 =9 π₯β10+18=9 π₯=1 1 6 β2 1 β5 β β28 (1, 2, β6)

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**Graph the solution to each inequality**

7π₯β3π¦>β9 Answer

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**Graph the solution to each inequality**

7π₯β3π¦>β9

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**Graph the solution to each inequality**

π₯βπ¦β€2 π¦<4π₯+1 Answer

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**Graph the solution to each inequality**

π₯βπ¦β€2 π¦<4π₯+1

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**Graph the solution to each inequality**

π¦β₯2 π₯β3 β4 π¦<β 2 3 π₯+1 Answer

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**Graph the solution to each inequality**

π¦β₯2 π₯β3 β4 π¦<β 2 3 π₯+1

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**Graph the feasible region and find the point that maximize the function: 3π₯β4π¦**

π¦β₯π₯β2 π₯+2π¦β€8 π¦β₯1 π₯β₯0 Answer

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**Graph the feasible region and find the point that maximizes the function: 3π₯β4π¦**

π¦β₯π₯β2 π₯+2π¦β€8 π¦β₯1 π₯β₯0 (0, 1) 3 0 β4 1 =β4 (0, 5) 3 0 β4 5 =β20 (4, 2) 3 4 β4 2 =4 (3, 1) 3 3 β4 1 =5

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**Graph the feasible region and find the point that maximizes the function: 4π₯+5π¦**

βπ₯+2π¦β€4 π₯+π¦β€8 π¦β₯1 π₯β₯2 Answer

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**Graph the feasible region and find the point that maximizes the function: 4π₯+5π¦**

βπ₯+2π¦β€4 π₯+π¦β€8 π¦β₯1 π₯β₯2 (2, 1) =13 (2, 2) =18 (5, 4) =40 (7, 1) =33

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The school that Danielle goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 7 senior citizen tickets and 3 child tickets for a total of $74. The school took in $135 on the second day by selling 14 senior citizen tickets and 5 child tickets. Write a system of equations to find the price of one senior citizen ticket and one child ticket? Answer

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**π=Senior Citizen Tickets πΆ=Child Tickets 7π+3πΆ=74 14π+5πΆ=135**

The school that Danielle goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 7 senior citizen tickets and 3 child tickets for a total of $74. The school took in $135 on the second day by selling 14 senior citizen tickets and 5 child tickets. Write a system of equations to find the price of one senior citizen ticket and one child ticket? π=Senior Citizen Tickets πΆ=Child Tickets 7π+3πΆ=74 14π+5πΆ=135

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Amanda and Eduardo each improved their yards by planting grass sod and shrubs. They bought their supplies from the same store. Amanda spent $83 on 7 ftΒ² of grass sod and 3 shrubs. Eduardo spent $118 on 8 ftΒ² of grass sod and 6 shrubs. Find the cost of one ftΒ² of grass sod and the cost of one shrub. Write a system of equation to solve the problem. Answer

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**πΊ=Grass Sod π=Shrubs 7πΊ+3π=83 8πΊ+6π=118**

Amanda and Eduardo each improved their yards by planting grass sod and shrubs. They bought their supplies from the same store. Amanda spent $83 on 7 ftΒ² of grass sod and 3 shrubs. Eduardo spent $118 on 8 ftΒ² of grass sod and 6 shrubs. Find the cost of one ftΒ² of grass sod and the cost of one shrub. Write a system of equation to solve the problem. πΊ=Grass Sod π=Shrubs 7πΊ+3π=83 8πΊ+6π=118

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**Meg has three dogs β Skippy, Gizmo, and Chopper**

Meg has three dogs β Skippy, Gizmo, and Chopper. The sum of the dogsβ weights is 148 pounds. If you add three times Skippyβs weight to Gizmoβs weight, the sum is 8 pounds less than Chopperβs weight. If you subtract one-third of Skippyβs weight from four times Gizmoβs weight, the result is equal to twice Chopperβs weight. Write a system of equations to find out how much each dog weighs? Then solve the system. Answer

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**π=Skippy πΊ=Gizmo πΆ=Chopper π+πΊ+πΆ=148 3π+πΊ=πΆβ8 4πΊβ 1 3 π=2πΆ**

Meg has three dogs β Skippy, Gizmo, and Chopper. The sum of the dogsβ weights is 148 pounds. If you add three times Skippyβs weight to Gizmoβs weight, the sum is 8 pounds less than Chopperβs weight. If you subtract one-third of Skippyβs weight from four times Gizmoβs weight, the result is equal to twice Chopperβs weight. Write a system of equations to find out how much each dog weighs? Then solve the system. π=Skippy πΊ=Gizmo πΆ=Chopper π+πΊ+πΆ=148 3π+πΊ=πΆβ8 4πΊβ 1 3 π=2πΆ Skippy: 12 pounds Gizmo: 46 pounds Chopper: 90 pounds

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You manage a health food store and budget $80 to buy ingredients to make 30 pounds of trail mix. Peanuts cost $2.50 per pound, raisins cost $2.00 per pound and granola cost $4.00 per pound. If you use twice as many pounds of peanuts as raisins, how many pounds of each ingredient should you buy? Answer

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**2.5π+2π+4π=80 π+π+π=30 π=2π Peanuts (p): 16 pounds**

You manage a health food store and budget $80 to buy ingredients to make 30 pounds of trail mix. Peanuts cost $2.50 per pound, raisins cost $2.00 per pound and granola cost $4.00 per pound. If you use twice as many pounds of peanuts as raisins, how many pounds of each ingredient should you buy? 2.5π+2π+4π=80 π+π+π=30 π=2π Peanuts (p): 16 pounds Raisins (r): 8 pounds Granola (g): 6 pounds

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**You are making your summer movie plans and are working with following constraints:**

It costs $8 to go to the movies at night. It costs $5 to go to a matinee. You want to go to at least as many night shows as matinees. You want to spend at most $42 What is the greatest number of movies you can see? Answer

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**8π+5πβ€42 πβ₯π πβ₯0 πβ₯0 6 Movies: 3 night, 3 matinee 4 night, 2 matinee**

You are making your summer movie plans and are working with following constraints: It costs $8 to go to the movies at night. It costs $5 to go to a matinee. You want to go to at least as many night shows as matinees. You want to spend at most $42 What is the greatest number of movies you can see? 8π+5πβ€42 πβ₯π πβ₯0 πβ₯0 6 Movies: 3 night, 3 matinee 4 night, 2 matinee

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