1. Lesson #22 - Systems of Equations

2. 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. GraphicallyTable of Values Algebraic Comparison let y 1 =y 2 solve for x check for y xy1y1 y2y2 290 455 6110 8-315 solution

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

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 1000x + 6000y = 600 000 # of items total value

6. 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 trophies Let y rep the # of cards 5x + 2y = 97 x + y = 32 total value # of items

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

8. 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 tank wheelbarrow

9. 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 1 Project 2

10. Homework Linear Systems Handout #2