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Solving by Graphing
Solving by Substitution
How many solutions
Word Problems
Isolate the y
100

y = 2x - 2

y=1/2x - 2

(0,-2)

100

y = 2x + 3

y = 5x

(1,5)

100

Without graphing or solving, determine the number of solutions to the system.  Explain your reasoning.

y = 5x - 9

y = 5x + 9

no solution;  the lines are parallel

100
You are purchasing a new iPhone. Verizon has a deal to buy the phone at the store for $100 and then pay $50 each month. If you buy online, you pay $200 and then pay $40 each month.

Write two equations to represent the two options.

y = 50x + 100

y = 40x + 200

100

2x + 3y = 6

y=-2/3x + 2

200

y = x + 1

y = 4x + 7

(-2,-1)

200

y=2x - 3

y=2x + 2

No solution

200

Without graphing or solving, determine the number of solutions to the system.  Explain your reasoning.

y = 6x + 2

y = 3x + 1

1 solution;  Different slopes

200

You and your brother and racing across the swimming pool. You give him a 5 second head start and he swims 2 meters per second. You swim at 3 meters per second. Write two equations to represent this situation.

y = 2x + 5

y = 3x

200

-x - 5y = -10

y= x + 2

300

y= 3x -1

y = x -5

(-2,-7)

300

y=x-13

y=-5x+5

(3,-10)

300

Without graphing or solving, determine the number of solutions to the system.  Explain your reasoning.

y = 8x - 2

y + 8x = -2

1 solution;  different slopes

300

Two classes are raising money for the animal shelter.

Mrs. Johnston's class raises money by selling donuts and make a profit of $1 per donut. They also received a donation of $12 from Mrs. Johnston.

Mrs. Schwartz's class raises money by washing cars for $3 per car.

Write AND solve the system of equations. 

y = 1x + 12

y = 3x

(6, 18)

300

3x + 7y = -21

y = -3/7x - 3

400

y = -4x - 7

y = -x + 2

(-3, 5)

400

y=x+9

y=-3x-15

(-6, 3)

400

Without graphing or solving, determine the number of solutions to the system.  Explain your reasoning.

4y - 4x= 8

y = x + 2

infinitely many solutions;  same equations

400
Which pizza shop would you purchase from if you want to order a pizza with 5 toppings? 


Shop A: A pizza costs $12 plus $1 per topping.

Shop B: A pizza costs $8 plus $2 per topping. 

Shop A

400

-2x - 6y = 10

y= -1/3x - 5/3

500

y = -4

x = 2

(2, -4)

500

x=-7

3x-5y=-16

(-7, -1)

500

Without graphing or solving, determine the number of solutions to the system.  Explain your reasoning.

2x - 4y = 10

-12x + 24y = -60

Infinitely many solutions;  same equation

500

Write and solve (using substitution) a system of equations for the following scenario:

A concert at Red Rocks costs $86 for a ticket, plus $5 per hour for parking. 

A concert at Ball Arena costs $100 for a ticket, plus $5 per hour for parking. 

No solution

500

-3x + 4y = -8

y= 3/4x - 2