Lesson #22 - Systems of Equations
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Transcript of Lesson #22 - Systems of Equations
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Lesson #22 - Systems of Equations
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A system of equations is a set of two or more equations with 2 variables.
The solution to a system is the point where two lines intersect.
Graphically Table of Values Algebraic Comparison
let y1=y2 solve for xcheck for y
x y1 y22 9 0
4 5 5
6 1 10
8 -3 15
solutionsolution
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Solving Systems
Step 1: Define variables and setup 2 equations
Step 2: Solve equation using the comparison method
Step 3: Do a check to confirm your answer
Step 4: Write a concluding statement
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(1) Mr. Harvey has a collection of pennies and nickels in his retirement fund. He has a total of 357 coins worth $7.93. How many coins of each type does Mr. Harvey have?
Let x rep the # of pennies Let y rep the # of nickels
x + y = 357
1x + 5y = 793
# of coinstotal cost
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(2) a) Define your variables b) Setup the TWO equations
Donald Trump has a collection of 1000 $ bills and bars of gold ($6000 each) in his retirement fund. He has a total of 300 items worth $600 000. How many of each item does Mr. Trump have?
Let x rep the # of 1000 $ billsLet y rep the # of bars of gold
x + y = 300
1000x + 6000y = 600 000
# of itemstotal value
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Your Mrs. Perrier gives out awards. She gives trophies ($5/each) and cards ($2/each). If she buys 32 awards in total costing $97 in all, how many trophies did she buy?
(3) a) Define your variables b) Setup the TWO equations
Let x rep the # of trophiesLet y rep the # of cards
5x + 2y = 97
x + y = 32
total value # of items
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A job as Santa pays the following.
We Love Christmas Co: $25 a day plus $3 per photoMilk and Cookies Co: $20 plus $4 per photo.
After how many photos do the two companies pay the same amount?
(4) a) Define your variables b) Setup the TWO equations
Let x rep the # of photosLet y rep Santa’s salary ($)
y = 3x+ 25
y = 4x + 20
Company 1Company 2
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A giant tank of eggnog is leaking! The tank contains 6500 L of eggnog and empties at a rate of 95 L/min. Workers find a giant wheelbarrow to hold the leaking liquid. If the wheelbarrow already contained 80 L of eggnog, when will the wheel barrow contain the same amount of liquid as the tank?
(5) a) Define your variables b) Setup the TWO equations
Let x rep the # of time (min)Let y rep volume of eggnog (L)
y = -95x+ 6500
y = 95x + 80
tankwheelbarrow
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A scientist worked for 6 days on a project and her assistant worked for 5 days, earning a total of $780. They earned $500 on the next project, which required 4 days work from the scientist and 3 days work from the assistant. How much money did each earn per day?
(6) a) Define your variables b) Setup the TWO equations
Let x rep the scientists daily salary ($)Let y rep the assistant’s daily salary ($)
6x + 5y = 780
4x + 3y = 500
Project 1Project 2
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HomeworkLinear Systems Handout #2