1. SOLVING SYSTEM OF EQUATIONS Unit 1

2. System of equations Define: system of equations- a set of two or more equations Define: solution of a system- ordered pair(s) that make all the equations true. Key concept: the solution to a system is where the graphs intersect. Lines intersect 1 solution Lines are Parallel No solution Lines coincide Infinitely many solutions

3. Solve by graphing Solve by graphing:  Graph in y=  2 nd,trace, intersection, enter, enter, enter

4. Solve a system by matrices There are other ways to solve a system besides graphing. One alternative way is using matrices. Matrices can be used to solve 2x2 systems and bigger. SOLVE the 3x3 system [2 nd ], [matrix],  edit, type in systems, [2 nd ], [quit] [2 nd ], [matrix],  MATH, rref, [A] The last column is your answer

5. System word problem Mr. Smith bought 2 lbs of jelly and 3 lbs of peanut butter. He paid $26.35. Mrs. Sing paid $18.35 for 1.5 lbs of jelly and 2 lbs of peanut butter. What was the price per pound of each item? 1 st write two equations that model the above situation. ~Mr. Smith’s shopping trip ~Mrs. Sing’s shopping trip Then solve the system by graphing. (use CALC)

6. System practice Pg 138 #7-14 Pg 172 #21, 23, 25, 30, 32

7. 3 x 3 extra practice

8. System of inequalities The solution to a system of inequalities is not where the graphs intersect but where the shaded region overlap! Your answer is the your graph and shaded region

9. System of inequalities Solve each system of inequalities

10. System of inequalities Extra practice: pg 153 # 11-13 & 22, 25,27

11. A pizza parlor charges $1 for each vegetable toppings and $2 for each meat toppings. You want at least 2 meat toppings on your pizza. You have $10 to spend on toppings. How many of each type of toppings can you get on your pizza? Extra practice: PG 152 # 4, 20,21,32

12. System of inequality word problem Kayla wants to buy Hotdogs, hamburgers, or some of each for weekend meals. The Hotdogs costs $4 per pound and the Hamburger costs $3 per pound. She will spend at least $11 but no more than $15. a. Write a system of inequalities to model the situation. b. Graph the system to show the possible amounts Kayla could buy. Answer 4x + 3y ≥ 11 4x + 3y ≤ 15 x ≥ 0 y ≥ 0 Extra practice: PG 152 # 4, 20,21,32

13. A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. What are the restrictions for Scientific and graphing calculators Extra practice: PG 152 # 4, 20,21,32