October 7: Systems of Equations Today you will review how to solve systems of equations by graphing and will learn how to classify the systems. - HW Review - New Turn in process - Get graph paper and rulers - Warm up & Notes - CW: p. 123 #25, 27, 29, 31 - A18: p. 123 #33, 37-40, 45-48, 56, 57 - Get tests back

Warm up – Do in your NOTES! 2 lines are drawn in a coordinate plane. What is the least number of points they can have in common? What is the most? Are there any other possibilities?

Oct 9 Warm up – do in notes! 1. Solve for x:2. Solve for x: 3. Classify the system without graphing (inconsistent, independent, dependent)

October 9: Solving without Graphing Warm up HW check Notes: Solving systems with Substitution and Elimination Methods CW: p. 130 #5, 17, 31, 43, 54-56, 60 A19: p. 130 #9, 11, 15, 19, 27, 35, 37, 42, 47, 68, 74, 76

October 11: Solving Systems HW check In class activity: Notebooks & Pens Partner Quiz A20: p. 130 #48-50 all, all, 69, 78

October 15: Systems of Inequalities; Linear Programming HW check Warm up – In Notes Systems of Inequalities Notes Linear Programming Notes A21: p. 138 #4-8, 13, 15-17, 30-34, 51 A22: p. 144 #1-9 odd, 20

Warm up – do in your NOTES How could you represent the solutions to these problems? 1) The sum of 2 numbers is 24. What are the numbers? 2) The sum of 2 numbers is 24. The second number is 10 more than the first. What are the numbers? 3) The sum of the 2 numbers is less than 24. What are the numbers?

3-3: Systems of Inequalities More than 1 inequality in the coordinate plane Example 1: The sum of 2 numbers is less than 24. The second number is at least 10 more than the first number. Write a system of inequalities and graph the solution. Is (2, 7) a solution? (check both equations when given a point)

Example 1: Graph solution

Example 2: Graph solution

Example 3: Write the system of inequalities for the figure below

Example 4: p. 137 CA Standards Check A college entrance exam has two parts, a verbal part and a mathematics part. The school requires a math score of at least 550 points and a total score of at least 1100 points. You can score up to 800 points on each part. Write and solve a system of inequalities to model scores that meet the school’s requirements.

Example 4: Graph the solution A college entrance exam has two parts, a verbal part and a mathematics part. The school requires a math score of at least 550 points and a total score of at least 1100 points. You can score up to 800 points on each part.

3-4 Linear Programming Linear Programming a technique used to find minimum and maximum values. Objective Function: A linear function that tells what you are trying to maximize or minimize. Constraints: Linear inequalities (the graph) Feasible Area/Region: Shaded area – Possible Answers If there is a min or max value of the linear objective function, it will occur at one or more of the vertices of the feasible region.

Example 1: p. 142 Steps 1. Graph the Constraints 2. Find coordinates for each vertex 3. Evaluate Objective Function at each vertex

October 21 New Seats HW Check Systems of 3 equations A23: p. 159 #1, 3, 9, 20, 21, 25, 27, 39, 40 PICK ANY 4 (one must be a word problem) Next time – Review Friday – Ch 3 test

3-6 Systems of 3 equations If 3 variables, must have 3 equations. Must solve for all 3 variables!

3-6 Systems of 3 equations High Level Steps Eliminate a variable. Get 2 equations with 2 variables. Solve for the 2 remaining variables. Substitute and solve for the 3 rd variable. Check!

A more complicated example 1. Number your equations 2. Decide which variable to eliminate 3. Combine 2 sets of equations to eliminate the variable (BOX) 4. Combine boxed equations together to eliminate another variable (CIRCLE) 5. Plug in circled answer to a Boxed equation to get 2 nd variable. (CIRCLE) 6. Plug both circled answers into an original equation to get 3 rd variable (CIRCLE) 7. Plug all 3 into all 3 equations to check. 8. State in alpha order (x, y, z)

What if one of the coefficients is 0?