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Simultaneous Equations: Substitution Method and Graph Plotting Lesson

Engage in a comprehensive lesson on solving simultaneous equations using the substitution method and graph plotting. Recap on elimination method and practice with various difficulty levels. Explore step-by-step examples and answer practice questions to master these techniques effectively.

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Simultaneous Equations: Substitution Method and Graph Plotting Lesson

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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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