1. 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
Let 𝑥=𝑠𝑝𝑜𝑜𝑛𝑠 Let 𝑦=𝑓𝑜𝑟𝑘𝑠
𝑥+𝑦=8
𝑥=5 spoons 𝑦=3 forks
5𝑥+6𝑦=43

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

3. Must Do: (11/30)
1. Solve by substitution. Check your answers. 𝑦=−𝑥+3 𝑥−2𝑦=0 Bonus! 2. Solve by substitution. Check your answers. 3𝑥−6𝑦+24=0 −6−2𝑦=−𝑥
𝑥=2 𝑦=1
Solution: (2, 1)
𝑁𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛.
The lines are parallel

4. Can We Make This Simpler?
Each equation is represented in an equations mat. 2𝑥+3𝑦=−2 5𝑥−3𝑦=16
Can these equations be combined to make a new equation?
Yes! x x y y y x x x x x y y y

5. We CAN Make it Simpler! These become this x x y y y x x x x x x x x x

6. Must Do: (12/1)
1. Solve by substitution. Check your answers. 2x=−𝑦+9 3𝑥=𝑦+16
Bonus!
2. Solve by substitution. Check your answers. −2𝑦−𝑥+4=0 6𝑦=−3𝑥+12
𝑥=5 𝑦=−1
Solution: (5, −1)
𝐼𝑛𝑓𝑖𝑛𝑖𝑡𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠.
The lines are the same

7. Must Do: (12/1) Algebra Review (Distribution and Factoring):
1. Solve: 8− 4−2𝑥 =−3(4𝑥−2)
2. Solve for x:
5𝑥−5 −2−𝑥𝑦 =−𝑥+3−3𝑥𝑦

8. 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.

9. 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

10. Example Solve the system using elimination 𝑥+3𝑦=−14 −4𝑥−3𝑦=2 𝑥=4 𝑦=−6
Solution: (4, −6)

11. Example Solve the system using elimination 5𝑥+2𝑦=12 −5𝑥+4𝑦=30 𝑥=− 2 5
𝑦=7
Solution: (− 2 5 , 7)

12. You Try! Solve the system using elimination −4𝑥−4𝑦=4 6𝑥+4𝑦=−8 𝑥=−2 𝑦=1
Solution: (−2, 1)

13. What If They Don’t Simplify Nicely?
Example: Solve using elimination 16𝑥−10𝑦=10 8𝑥+6𝑦=−6
Use the multiplicative property of equality!
So now we have: 16𝑥−10𝑦=10 −2 8𝑥+6𝑦 =−2 −6
Which becomes: 16𝑥−10𝑦=10 −16𝑥−12𝑦=12
𝑥=0 𝑦=−1
Solution: (0, −1)

14. Example
Solve the system using elimination. Multiply an equation by a common factor if necessary. 8𝑥+14𝑦=4 −6𝑥−7𝑦=−10
𝑥=4 𝑦=−2
Solution: (4, −2)

15. You Try!
Solve the system using elimination. Multiply an equation by a common factor if necessary. −4𝑥−15𝑦=−17 −𝑥+5𝑦=13
𝑥=8 𝑦=−1
Solution: (8, −1)

16. In Class Practice
U4D11 - ICP

17. Must Do: (12/3)
1. Solve by elimination. Check your answers. 3𝑥−𝑦=5 𝑥+𝑦=3
Bonus!
2. Solve by elimination. Check your answers. −4𝑥−15𝑦=−17 −𝑥+5𝑦=13
𝑥=5 𝑦=−1
Solution: (5, −1)

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

19. 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

20. 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.

21. 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

22. Must Do: (12/8)
Solve the system of equations using elimination. Check your work
2𝑥 − 3𝑦=−12
−3𝑥+4𝑦=10
(18,16)
2. Solve the system of equation using elimination. Check your work. − 1 2 𝑥+𝑦=−3 2𝑦+𝑥=25
(31/2, 19,4)