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October 7: Systems of Equations

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

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October 7: Systems of Equations

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  1. 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

  2. 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?

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

  4. 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

  5. October 11: Solving Systems • HW check • In class activity: Notebooks & Pens • Partner Quiz • A20: p. 130 #48-50 all, 57-63 all, 69, 78

  6. 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

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

  8. 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)

  9. Example 1: Graph solution

  10. Example 2: Graph solution

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

  12. 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.

  13. 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.

  14. 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.

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

  16. 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

  17. 3-6 Systems of 3 equations • If 3 variables, must have 3 equations. • Must solve for all 3 variables!

  18. 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 3rd variable. Check!

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

  20. What if one of the coefficients is 0?

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