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Equations

Equations. Objectives for today’s lesson : Recap on solving SE’s using elimination Solving SE’s using substitution. Starter. Choose two of these problems to solve : 3x + y = 21 Easy x + y = 11 4x + 2y = 24 Medium 3x + y = 14 2x + 3y = 27 Hard 3x + 2y = 23. Starter.

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Equations

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  1. Equations Objectives for today’s lesson : • Recap on solving SE’s using elimination • Solving SE’s using substitution

  2. Starter Choose two of these problems to solve : 3x + y = 21 Easy x + y = 11 4x + 2y = 24 Medium 3x + y = 14 2x + 3y = 27 Hard 3x + 2y = 23

  3. Starter Choose two of these problems to solve : 3x + y = 21 x = 5, y = 6 x + y = 11 4x + 2y = 24 x = 2, y = 8 3x + y = 14 2x + 3y = 27 x = 3, y = 7 3x + 2y = 23

  4. Using substitution There is another way to solve simultaneous equations : Example : x – 3y = 14 (1) x + y = 22 (2)

  5. Using substitution There is another way to solve simultaneous equations : Example : x – 3y = 14 (1) x + y = 22 (2) Rearrange equation (1)

  6. Using substitution There is another way to solve simultaneous equations : Example : x – 3y = 14 (1) x + y = 22 (2) Rearrange equation (1) x = 14 + 3y

  7. Using substitution There is another way to solve simultaneous equations : Example : x – 3y = 14 (1) x + y = 22 (2) Rearrange equation (1) x = 14 + 3y Now, substitute this in equation (2)

  8. Using substitution There is another way to solve simultaneous equations : Example : x – 3y = 14 (1) x + y = 22 (2) Rearrange equation (1) x = 14 + 3y Now, substitute this in equation (2) 14 + 3y + y = 22

  9. Using substitution There is another way to solve simultaneous equations : Example : x – 3y = 14 (1) x + y = 22 (2) Rearrange equation (1) x = 14 + 3y Now, substitute this in equation (2) 14 + 3y + y = 22 So, 14 + 4y = 22

  10. Using substitution There is another way to solve simultaneous equations : Example : x – 3y = 14 (1) x + y = 22 (2) Rearrange equation (1) x = 14 + 3y Now, substitute this in equation (2) 14 + 3y + y = 22 So, 14 + 4y = 22 4y = 8 y = 2

  11. Substitution Question Practice x + 3y = 31 x + y = 13 x + 5y = 51 x + y = 11 x + 4y = -3 x + 2y = 1

  12. Substitution Question Practice - Answers x + 3y = 31 x = 4, y = 9 x + y = 13 x + 5y = 51 x = 1, y = 10 x + y = 11 x + 4y = -3 x = 5, y = -2 x + 2y = 1

  13. To finish There is one final way of solving these equations. To do this, you need to be able to plot straight line graphs.

  14. To finish Plot these straight line graphs : y = x y = 2x + 1 y = 1 - x y = 3x – 1

  15. To finish y = x y = 2x + 1 y = 1 - x y = 3x - 1

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