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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 823 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.2x + 4y = 24 and 5x + 2y = 44 →
  2. 2.x − 4y = −16 and 4x + 6y = 46 →
  3. 3.4x + 6y = 22 and 6x + 4y = 28 →
  4. 4.3x + 3y = 27 and 3x + 4y = 31 →
  5. 5.5x + y = 39 and 5x − 4y = 44 →
  6. 6.8x + 2y = 30 and 2x + 8y = 60 →
  7. 7.4x + 5y = 57 and 5x + 5y = 65 →
  8. 8.x + 9y = −67 and 9x + y = −43 →
  9. 9.5x + 2y = 13 and 4x − 3y = −8 →
  10. 10.8x + 4y = 96 and 4x + 8y = 96 →
  11. 11.x + 2y = −9 and 4x + y = −15 →
  12. 12.2x − 3y = −15 and 2x − y = 3 →
  13. 13.2x + 6y = 40 and 2x + 5y = 35 →
  14. 14.4x − y = 29 and 5x − 5y = 70 →
  15. 15.6x + 2y = −20 and 2x + 6y = 36 →
  16. 16.4x + 6y = −12 and 3x − y = −20 →
  17. 17.3x + y = 16 and 5x + 4y = 22 →
  18. 18.x + y = −7 and 2x + 6y = −30 →
  19. 19.3x + 6y = 15 and 5x + y = 43 →
  20. 20.5x + 4y = −31 and 2x + y = −13 →
  21. 21.2x − 6y = −52 and 2x + 3y = 29 →
  22. 22.3x + 2y = 4 and 2x + 3y = 1 →
  23. 23.6x − 4y = 30 and 4x − 6y = 40 →
  24. 24.3x − 3y = −12 and 2x + 5y = −1 →
  25. 25.9x + 5y = 61 and 5x + 9y = 65 →
  26. 26.6x + 5y = −21 and x + y = −3 →
  27. 27.2x + 6y = −22 and 2x − 2y = 10 →
  28. 28.2x + 7y = −37 and 7x + 2y = −17 →
  29. 29.8x + 2y = 48 and 2x + 8y = 72 →
  30. 30.6x − 6y = −6 and 4x + 6y = −44 →
  31. 31.4x + 8y = −68 and 8x + 4y = −40 →
  32. 32.6x + 2y = 42 and 2x + 6y = 30 →
  33. 33.2x + 4y = −12 and 2x + 6y = −24 →
  34. 34.6x + y = −51 and 5x + 3y = −36 →
  35. 35.5x + 6y = 13 and 6x + 5y = 9 →
  36. 36.5x + 6y = 87 and x + 3y = 30 →
  37. 37.6x + 4y = 30 and x − 5y = 39 →
  38. 38.4x − 2y = 28 and 6x + 3y = 18 →
  39. 39.x − 4y = −10 and x − 6y = −12 →
  40. 40.4x − 3y = 7 and 4x + y = −13 →

Answer key

  1. x = 8, y = 2
  2. x = 4, y = 5
  3. x = 4, y = 1
  4. x = 5, y = 4
  5. x = 8, y = −1
  6. x = 2, y = 7
  7. x = 8, y = 5
  8. x = −4, y = −7
  9. x = 1, y = 4
  10. x = 8, y = 8
  11. x = −3, y = −3
  12. x = 6, y = 9
  13. x = 5, y = 5
  14. x = 5, y = −9
  15. x = −6, y = 8
  16. x = −6, y = 2
  17. x = 6, y = −2
  18. x = −3, y = −4
  19. x = 9, y = −2
  20. x = −7, y = 1
  21. x = 1, y = 9
  22. x = 2, y = −1
  23. x = 1, y = −6
  24. x = −3, y = 1
  25. x = 4, y = 5
  26. x = −6, y = 3
  27. x = 1, y = −4
  28. x = −1, y = −5
  29. x = 4, y = 8
  30. x = −5, y = −4
  31. x = −1, y = −8
  32. x = 6, y = 3
  33. x = 6, y = −6
  34. x = −9, y = 3
  35. x = −1, y = 3
  36. x = 9, y = 7
  37. x = 9, y = −6
  38. x = 5, y = −4
  39. x = −6, y = 1
  40. x = −2, y = −5

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