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Special Systems
Solving by Graphing
Solving by Elimination
Solving by Substitution
Word Problems
100
This type of system has no solution.
What is inconsistent?
100
Tell whether the ordered pair is a solution to the system. (-2,1) y=-2x-3 y=x+3
Yes, it is a solution.
100
What should the equations have if you are going to add them together? What about subtract?
Add- opposite coefficients Subtract- same coefficients
100
True or false: Both equations need to be solved for a variable before you can use substitution.
False, you only need to solve one!
100
Solve using any method. Michael breeds chickens and ducks. Last month, he sold 50 chickens and 30 ducks for $550. This month, he sold 44 chickens and 36 ducks for $532. How much does a chicken cost, and how much does a duck cost?
Chicken is $8 Duck is $5
200
This type of system has at least one solution.
What is consistent?
200
Tell whether the ordered pair is a solution to the system. (9,2) x-4y=1 2x-3y=3
No, it is not a solution.
200
How can we tell if we should multiply the equations first?
If you don't have opposite coefficients, you should multiply one or both of the equations so you do.
200
Solve by substitution. y=2x y=x+5
(5,10)
200
A shopper bought 6 shirts and 8 hats for $700. A week later, at the same prices, he bought 9 shirts and 6 hats for $660. What was the cost of one shirt?
$30
300
What are the subsets of consistent systems and what do they mean?
Independent- Exactly one solution Dependent- Infinitely many solutions
300
Solve the system by graphing. y=x+5 y=1/2x+4
(-2,3)
300
Solve by elimination. x-2y=-19 5x+2y=1
(-3,8)
300
Solve by substitution. 2x+y=5 y=x-4
(3,-1)
300
Liam's bookstore sold 40 notebooks and 20 newspapers for a total of $130. A day later, the bookstore sold 8 notebooks and 4 newspapers at the same prices, for a total of $28. How much does a notebook and a newspaper cost at Liam's bookstore?
Notebook=$1.50 Newspaper=$2.50
400
Classify the system. y=-4x+2 4x+y=-2
Inconsistent (no solution)
400
Solve the system by graphing. y=-x-2 2x-y=2
(0,-2)
400
Solve by elimination. 3x+4y=18 -2x+4y=8
(2,3)
400
Solve by substitution. x+4y=6 x+y=3
(2,1)
400
A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totaled $232. The bills do not list the per-item price. What were the costs of one bush and of one tree?
Bushes=$23 Trees=$47
500
Classify the system. 4x-3y=8 y=4(x+2)
Consistent and dependent. Bonus 100 points: Solve the system
500
Solve the system by graphing. 2/3x+y=-3 4x+y=7
(3,-5)
500
Solve by elimination. 7x-12y=-22 5x-8y=-14
(2,3)
500
Solve by substitution. 4y-5x=9 x-4y=11
(-5,-4)
500
Michaela’s mom is trying to decide between two plumber companies to fix her sink. The first company charges $50 for a service call, plus an additional $36 per hour for labor. The second company charges $35 for a service call, plus an additional $39 per hour of labor. At how many hours will the two companies charge the same amount of money? How much will it be?
5 hours, $230