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. 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)

5. 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

6. System of inequalities Solve each system of inequalities

7. System of inequalities

8. System of inequality word problem Leyla wants to buy fish, chicken, or some of each for weekend meals. The fish costs $4 per pound and the chicken 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 Leyla could buy. Answer 4x + 3y ≥ 11 4x + 3y ≤ 15 x ≥ 0 y ≥ 0

9. 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