Solve by 2nd Trace 5
Types of Systems
Writing Equations
Vocab
100
y = 2x + 5
y = -x - 4
(-3, -1)
100
How many solutions does the following system have?
y = 3x - 5
y = 1 + 3x
none -- the lines will never cross
100
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined.
Write 2 equations, but DO NOT SOLVE.
1.50x + 0.50y = 78.50
x + y = 87
100
When graphing a system of equations, the solution is the point of __________________ .
intersection
200
y = 1/2x
y = -2x + 5
(2,1)
200
The cost of three notebooks and four pencils is $8.50. The cost of five notebooks and eight pencils is $14.50. Write and a system where x is the cost of a notebook and y is the cost of a pencil
3x + 4y = 8.50
5x + 8y = 14.50
200
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You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos.
Write 2 equations, but DO NOT SOLVE.
200
What does a system that has no solution look like?
parallel lines
300
y = 4x - 1
y = 4x + 5
No solution
300
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Two hundred tickets were sold for a school concert. Students paid $2 and adults paid $5.
The total sales came to $670.
Write a system where x is the # of student tickets and y is the # of adults tickets sold
300
A farmhouse shelters 10 animals, some are pigs, and some are ducks. Altogether there are 36 legs. How many pigs are there?
Write the equations and solve.
p + g = 10
4p + 2d = 36
4 pigs and 10 ducks
300
What is the name for how we write the solution to a system? What do we call (x, y)?
Ordered pair
or coordinates
400
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2y = 4x - 6
-3y = x - 5
400
Company A is offering Jakob a job paying $8 per hour and a one-time $100 sign-on bonus.
Company B is offering to pay $8.50 an hour and a one-time $80 bonus.
Write two functions, A(x) and B(x), to represent the total amount Jakob could earn with
each company.
a(x) = 8x + 100
b(x) = 8.50x + 80
400
A man has 14 coins in his pocket, all of which are dimes ($0.10) and quarters ($0.25). If the total value of his change is $2.75, how many dimes and how many quarters does he have?
Write a system
d + q = 14
.10d + .25q = 2.75
400
The 2 equations in a system have the same slope and y-intercept.
What is the number of solutions for this type of system?
infinitely many
500
x + y = 3
2x + 2y = 6
Infinite solutions
500
At a concession stand, a pickle and two bags of chips costs a total of $3.25. Three pickles and four bags of chips costs a total of $7.25. To determine the cost of one pickle, Kevin is writing a system of equations. His first equation is
x+2y=3.25
What would the second equation be?
3x+4y=7.25
500
At a store, Eva bought two shirts and five hats for $154.00. Nicole bought three same shirts and four same hats for $168.00. What is the price of each shirt? _
SOLVE THE SYSTEM
2s + 5h = 154
3s + 4h = 168
shirts = $32
hats = $18
500
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This is the name for the STYLE our equations need to be in to use the calculator.
Hint: s______ - i___________ form