Lesson #22 - Systems of Equations

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

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

(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

(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

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

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

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

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

HomeworkLinear Systems Handout #2