1. Systems of Equations: Substitution
A system of equations refers to multiple equations involving multiple variables
A solution is an ordered pair that satisfies both equations.
(2,1) is the solution to the system 1 1

2. One method for solving a system of equations is substitution
Solve for a variable in one equation, and then plug into the other equation and solve
Find the value of the other variable by using one of the original equations

3. Ex. Solve the system

4. Ex. A total of $12,000 is invested in two funds paying 5% and 3% simple interest [I = prt]. If the yearly interest is $500, how much was invested at each rate?

5. Ex. Solve the system

6. Ex. Solve the system

7. One solution: graphs intersect once
Two solutions: graphs intersect twice
No solutions: graphs don't intersect

8. Ex. Solve the system by graphing

9. Ex. A shoe company invests $300,000 in equipment to produce a line of shoes. Each pair costs $5 to produce and is sold for $60. How many pairs of shoes must be sold before the business breaks even?

10. Ex. The weekly ticket sales, S, in millions, for a comedy movie are modeled by the equation S = 60 – 8x, and the sales model for a drama is S = x, where x is number of weeks that the movie plays. After how many weeks will the two movie sales be equal?

11. Practice Problems
Section 6.1
Problems 5, 19, 25, 27, 35, 63 11 11

12. Systems of Equations: Elimination
We are allowed to add the two equations in a system
By manipulating the coefficients, we can eliminate a variable and make the system easier to solve 12 12

13. Ex. Solve the system

14. Method of Elimination
Using multiplication, get the coefficients of a variable to be opposites
Add the equations to eliminate a variable
Solve for one variable, then use one of the original equations to find the other variable.

15. Ex. Solve the system

16. Ex. Solve the system

17. Ex. Solve the system
These graphs coincide

18. Ex. Solve the system
These graphs are parallel

19. Ex. Solve the system

20. Ex. A plane flies into a headwind while making a mile flight, which takes 4 hr 24 min. If the return flight takes 4 hr, find the plane's airspeed and the speed of the wind.

21. Practice Problems Section 6.2 Problems 11, 13, 15, 19, 23, 25, 43 21