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Mastering Systems of Equations in Math Class

Learn to solve systems of equations through graphing, classification, and advanced methods. Practice with engaging activities and real-world scenarios.

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Mastering Systems of Equations in Math Class

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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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