1 / 10

Lesson #22 - Systems of Equations

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 y 1 =y 2. solution. solve for x. solution.

Download Presentation

Lesson #22 - Systems of Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lesson #22 - Systems of Equations

  2. A systemof 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 solution solve for x solution check for y

  3. 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

  4. (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 # of coins x + y = 357 total cost 1x+ 5y = 793

  5. (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 $ bills Let y rep the # of bars of gold x + y = 300 # of items total value 1000x+ 6000y = 600 000

  6. (3) a) Define your variables b) Setup the TWO equations 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? Let x rep the # of trophies Let y rep the # of cards 5x + 2y = 97 total value # of items x + y = 32

  7. (4) a) Define your variables b) Setup the TWO equations A job as Santa pays the following. We Love Christmas Co:$25 a day plus $3 per photo Milk and Cookies Co: $20 plus $4 per photo. After how many photos do the two companies pay the same amount? Let x rep the # of photos Let y rep Santa’s salary ($) y = 3x+ 25 Company 1 Company 2 y = 4x + 20

  8. (5) a) Define your variables b) Setup the TWO equations 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? Let x rep the # of time (min) Let y rep volume of eggnog (L) y = -95x+ 6500 tank wheelbarrow y = 95x + 80

  9. (6) a) Define your variables b) Setup the TWO equations A scientist worked for 6 days on a project and her assistant worked for 5 days, earning a total of $780. They earned $500 on the next project, which required 4 days work from the scientist and 3 days work from the assistant. How much money did each earn per day? Let x rep the scientists daily salary ($) Let y rep the assistant’s daily salary ($) 6x + 5y = 780 Project 1 Project 2 4x + 3y= 500

  10. Homework Linear Systems Handout #2

More Related