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Algebra 2 Lesson 3.4

Algebra 2 Lesson 3.4. Check: p. 171 # 3, 7, 13, 21, 23. Test Chapter 3 Day after tomorrow. Section 3.4. Objective: Solve a system of linear equations in 3-variables. Systems of Three Equations. Example 1. 2x + 3y - 5z = 13. - 5y + z = -1. 3z = 12.

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Algebra 2 Lesson 3.4

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  1. Algebra 2Lesson 3.4 Check: p. 171 # 3, 7, 13, 21, 23 Test Chapter 3 Day after tomorrow

  2. Section 3.4 Objective: Solve a system of linear equations in 3-variables

  3. Systems of Three Equations

  4. Example 1 2x + 3y - 5z = 13 - 5y + z = -1 3z = 12 I think I’ll do some substitution.

  5. 2x + 3y - 5z = 13 - 5y + z = -1 3z = 12 3z = 12 z = 4 2x + 3(1) – 5(4) = 13 2x + 3 – 20 = 13 2x - 17 = 13 - 5y + 4 = -1 2x = 30 - 5y + 4 = -1 - 5y = -5 x = 15 y = 1 (15, 1, 4)

  6. Example 2 2x + 5y + 8z = 8 3x - 2y + 4z = 26 2x + 4y + 3z = -3 Let’s eliminate the y variable. Decide which variable you want to eliminate.

  7. 2x + 5y + 8z = 8 2 3x - 2y + 4z = 26 2 5 2x + 4y + 3z = -3 4x + 10y + 16z = 16 6x - 4y + 8z = 52 15x - 10y + 20z = 130 2x + 4y + 3z = -3 19x + 36z = 146 8x + 11z = 49 )19 ) ( -8( -152x - 288z = -1168 19x + 36(3) = 146 152x + 209z = 931 19x = 38 -79z = -237 x = 2 z = 3 2(2) + 5y + 8(3) = 8 4 + 5y + 24 = 8 (2, -4, 3) 5y = -20 y = -4

  8. Example 3 5x + 2y + 7z = 19 3x - 3y + 5z = 34 x + 3y - 5z = -22 Let’s eliminate the y variable. Decide which variable you want to eliminate.

  9. 5x + 2y + 7z = 19 3 3x - 3y + 5z = 34 2 x + 3y - 5z = -22 4x =12 15x + 6y + 21z = 57 x=3 6x - 6y + 10z = 68 21x + 31z = 125 21(3) + 31z = 125 31z = 62 z = 2 5 (3) + 2(y) + 7(2) = 19 15 + 2y + 14 = 19 (3, -5, 2) 2y = -10 y = -5

  10. Example 4 2x + 3y - 5z = -12 4x - 5y + 3z = 12 2x - 3y = -7 Let’s eliminate the z variable. Decide which variable you want to eliminate.

  11. 2x + 3y - 5z = -12 3 4x - 5y + 3z = 12 5 2x - 3y = -7 )-13 ( 6x + 9y - 15z = -36 20x - 25y + 15z = 60 26x - 16y = 24 ) ( 26x – 16(5) = 24 26x - 16y = 24 26x – 80 = 24 -26x + 39y = 91 26x = 104 23y = 115 x = 4 y = 5 2(4) + 3(5) – 5z = -12 8 + 15 – 5z = -12 (4, 5, 7) -5z = -35 z = 7

  12. Decide which variable to eliminate-- (-3, 4, 1)

  13. Application (Extra Example 4 Margin, p. 181) • At a carry-out pizza restaurant, an order of 3 slices of pizza, 4 bread sticks and 2 drinks costs $13.35. A second order of 5 slices of pizza, 2 breadsticks, and 3 drinks costs $19.50. If 4 bread sticks and a drink cost $0.30 more than a slice of pizza, what is the cost of each item?

  14. Application (Extra Example 4 Margin, p. 181) 3p + 4b + 2d = 13.35 5p + 2b + 3d = 19.50 4b + d = p + 0.30 (rearrange) -p + 4b + d = 0.30 Pizza: $2.95 Breadstick: $0.50 Drink: $1.25

  15. Assignments Classwork: p. 182 # 8, 14, 46 [#46 hint—eliminate the decimals first] Homework: p. 182 #3-5, 31-33, 42

  16. closure Identify your variables and write the system of equations. Start #42 (word problem)

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