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Solving Word Problems: Linear Systems | Three-Variable Equations

Learn to solve linear systems with 3 variables algebraically. Practice finding boat speeds and number problems.

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Solving Word Problems: Linear Systems | Three-Variable Equations

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  1. SWBAT: Solve systems of linear equations in three variables algebraically. Day 6 3 variable Systems

  2. SWBAT: Solve word problems using linear systems. Warm Up – REVIEW NOT IN PACKET! 2.) A boat traveled 200 miles downstream and back. The trip downstream took 10 hours. The trip back took 40 hours. Find the speed of the boat in still water and the speed of them current.

  3. SWBAT: Solve word problems using linear systems. t = tens digit u = ones digit = 18 Original number = 10t + u Reversed number = 10u + t 10t + u + 63 = 10u + t t + u = 9 t - u = -7 9t + 63 = 9u t + 7 = u 2t = 2 t = 1 u = 8

  4. SWBAT: Solve word problems using linear systems. 2.) A boat traveled 200 miles downstream and back. The trip downstream took 10 hours. The trip back took 40 hours. Find the speed of the boat in still water and the speed of them current. Downstream d=rt 200=10r 20=r 20 mph Upstream d=rt 200=40r 5=r 5 mph v + c = 20 v – c = 5 2v = 25 v = 12.5 mph c = 7.5 mph

  5. SWBAT: Solve word problems using linear systems. HW ANSWERS: (Page 35) 1.) v = 66mph and c = 22 mph 2.) v = 78 mph and c = 26 mph 3.) 84 5.) v = 14 mph and c = 10 mph 6.) 97

  6. SWBAT: Solve word problems using linear systems. Warm Up (Page 14) x = larger # y = smaller # x + y = 5 22 + y = 5 x – y = 39 y = -17 2x = 44 x = 22

  7. SWBAT: Solve word problems using linear systems. Warm Up (Page 37)

  8. SWBAT: Solve word problems using linear systems. Example 1 (Page 37)

  9. SWBAT: Solve word problems using linear systems. Example 1 (Page 15) 2x + y + z = 15 2x + y + z = 15 6x - 3y - z = 35 -4x + 4y - z = -14 8x - 2y = 50 -2x + 5y = 1

  10. SWBAT: Solve word problems using linear systems. Example 1 (Page 15) 8x - 2y = 50 8x - 2y = 50 4( ) -2x + 5y = 1 -8x + 20y = 4 18y = 54 y = 3 x = 7

  11. SWBAT: Solve word problems using linear systems. Example 1 (Page 15) y = 3 2x + y + z = 15 x = 7 2(7) + 3 + z = 15 17 + z = 15 z = -2

  12. SWBAT: Solve word problems using linear systems. Example 2 (Page 15) 4x + y - 3z = -6 -4( ) 4x + y - 3z = -6 5x - y - 7z = -19 -16x - 4y + 12z = 24 9x - 10z = -25 -2x + 4y + 2z = 38 -18x + 14z = 62

  13. SWBAT: Solve word problems using linear systems. Example 2 (Page 15) 2( ) 9x - 10z = -25 18x - 20z = -50 -18x + 14z = 62 -18x + 14z = 62 -6z = 12 z = -2 x = -5 y = 8

  14. SWBAT: Solve word problems using linear systems. Example 2 (Page 15)

  15. SWBAT: Solve systems of linear equations in three variables algebraically. Day 3 3 variable Systems Day 2

  16. SWBAT: Solve word problems using linear systems. Example 3 (Page )

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