1. 8.1 Systems of Equations in Two Variables Day 1 Do Now Solve for y 1) X – y = 5 2) 2x + y = 1

2. System of Equations There are three ways to solve a system of equations in two variables: – Graphing – Substitution – Elimination

3. Solving by Graphing When graphing a system of equations, the solution is the intersection – 1 solution: 1 intersection – 0 solutions: parallel lines – Infinitely many solutions: lines are identical

4. Ex Solve by graphing

5. Substitution Method 1) Solve equation 1 for one variable 2) Substitute equation 1 into equation 2 3) Solve for remaining variable 4) Solve for 2 nd variable

6. Ex Solve using substitution

7. Elimination Method 1) Multiply both equations by constants so that one pair of variables have the same coefficient 2) Add or subtract equations to eliminate 1 variable 3) Solve for the remaining variable 4) Solve for the 2 nd variable

8. Ex Solve using the elimination method

9. Ex Solve

10. Ex Solve

11. Ex Solve

12. Closure Solve HW: p.688 #1-37 odds

13. 8.1 Systems of Equations in Two Variables Day 2 Do Now Solve

14. HW Review: p.688 #1-37 odds

15. Applications When approaching a word problem, and there are 2 different measurements, you want to write one equation for each measurement

16. Ex At SnackMix.com, caramel corn worth $2.50 per pound is mixed with honey roasted mixed nuts worth $7.50 per pound in order to be 20 lbs of a mixture worth $4.50 per pound. How much of each snack is used?

17. Ex Kerry’s motorboat takes 3 hr to make a downstream trip with a 3mph current. The return trip against the same current takes 5 hr. Find the speed of the boat in still water

18. Ex The price and supply of a satellite radio are related by the equation y = 90 + 30x The price and demand of the radio are related by the equation y = 200 – 25x The equilibrium point for this product is when both are equal. Find the equilibrium point

19. Closure College students spend a total of $819 on textbooks and computer equipment. They spend $183 more on textbooks than on computer equipment. How much do they spend on each one? HW: p.689 #41-61 odds

20. 8.1 Systems of Equations Day 3 Do Now Jackson Manufacturing offers its sales reps a choice between being paid a commission of 8% sales or being paid a monthly salary of $1500 plus a commission of 1% of sales. For what monthly sales do the two plans pay the same amount?

21. HW Review: p.689 #41-61

22. Closure How do you solve a system of equations in 2 variables? Which method do you prefer? Why? HW: none