Must Do Identify the constraints write a system

Must Do • Identify the constraints, write a system of equations to represent this situation, then solve using substitution. – Maria bought 8 eating utensils for a total cost of $43. Spoons cost $5 and forks cost $6. How many of each eating utensil did she buy? – Constraints: 8 items, $5 spoons, $6 forks, $43 spent

Math 8 C Unit 4 – Day 11 Standards: ü Identify constraints and write a system of equations for a context. ü Use elimination to solve systems of equations.

Must Do: (11/30) •

Can We Make This Simpler? • y x x y y y x

We CAN Make it Simpler! • These become this y x x y y x x x y y y x x x

Must Do: (12/1) •

Must Do: (12/1) •

Solving Systems of Equations by Elimination • When graphing or substitution seem too messy, we can use another method called Elimination. • Elimination is where we eliminate a term by combining/adding two equations into a new one with only one variable.

Solving Systems of Equations by Elimination • Need equations to be in identical form: – Slope-intercept or – Standard or…. . . • Always add the two equations – Never subtract

Example •

Example •

You Try! •

What If They Don’t Simplify Nicely? •

Example •

You Try! •

In Class Practice U 4 D 11 - ICP

Must Do: (12/3) •

Solving Systems of Equations Word Problems Steps: 1. Define your variables. – Ex. x= or y= 2. Write your equations. – There should be 2! 3. Solve your system of equations – Use substitution, elimination, or graphing

Write a System and Solve • There are 7 animals in the field. Some are cows and some are chickens. Mmmm chicken. There are 22 legs among them. How many of each animal are there? – What are the variables and equations? – Solution? • 4 cows, 3 chickens

Write a System and Solve • Joan spent $570 on books for school. Math books cost $80 and science books cost $50. If she bought nine books altogether, how many of each kind did she buy? – What are the variables and equations? – Solution? • 4 math books and 5 science books.

Must Do: (12/7) Suppose you bought supplies for a party. Three rolls of streamers and 15 party hats cost $30. Later, you bought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers cost? How much did each party hat cost? A roll of streamer is $2. 50, party hats are $1. 50 each Challenge! A man is three times as old as his son was at the time when the father was twice as old as his son will be two years from now. Find the present age of each if they sum to 55. Father is 39 years old, Son is 16

Must Do: (12/8) (18, 16) • (31/2, 19, 4)