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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 643 · 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. 1.3x + 4y = −12 and 4x + 3y = −23 →
  2. 2.6x + y = −17 and x + 6y = −32 →
  3. 3.6x − 5y = 31 and 6x − 4y = 32 →
  4. 4.x + 2y = 1 and x + y = −1 →
  5. 5.x + 5y = −29 and x + 4y = −25 →
  6. 6.4x − 5y = −11 and 3x + 2y = −14 →
  7. 7.5x + 6y = 6 and 6x + 5y = −6 →
  8. 8.3x + 6y = −33 and 6x − 5y = 36 →
  9. 9.3x + 6y = 72 and 4x − 2y = 16 →
  10. 10.7x + 8y = 83 and 8x + 7y = 82 →
  11. 11.x + 4y = 15 and 4x + 5y = −6 →
  12. 12.x + 3y = −11 and 4x + 5y = −37 →
  13. 13.6x − 4y = −6 and 5x + 6y = 23 →
  14. 14.5x + 3y = 39 and 3x + 5y = 33 →
  15. 15.5x + y = −36 and x + 5y = −12 →
  16. 16.4x − 5y = −27 and 2x + 2y = 18 →
  17. 17.x + 2y = 12 and 2x + y = 15 →
  18. 18.5x + 2y = −43 and x + 2y = −7 →
  19. 19.4x − 2y = 38 and x + 4y = −13 →
  20. 20.6x + 5y = 93 and 5x + 6y = 94 →
  21. 21.5x − y = 0 and 2x + 2y = 12 →
  22. 22.2x − y = 4 and 3x − 2y = 3 →
  23. 23.6x + 6y = 54 and 5x + 4y = 40 →
  24. 24.3x + 4y = 44 and 4x + 4y = 52 →
  25. 25.4x + 2y = 42 and 4x + y = 35 →
  26. 26.2x + 9y = 55 and 9x + 2y = 55 →
  27. 27.x + 3y = 10 and 2x + y = 5 →
  28. 28.x − 5y = −42 and 4x − 3y = −32 →
  29. 29.2x − 3y = 5 and 6x − 3y = 21 →
  30. 30.x + 3y = 11 and x − 6y = 2 →
  31. 31.x − 4y = −20 and 4x − 3y = −28 →
  32. 32.3x − 4y = −1 and 6x + 4y = −62 →
  33. 33.5x + 6y = 20 and 6x + 5y = 13 →
  34. 34.5x + 2y = 29 and x + y = 10 →
  35. 35.5x + 3y = 23 and 6x + y = 38 →
  36. 36.5x + y = 2 and 4x + 4y = 24 →
  37. 37.5x + y = −47 and x + 5y = −19 →
  38. 38.6x + 2y = 48 and 2x − 5y = −35 →
  39. 39.6x + 4y = −14 and x + 3y = −21 →
  40. 40.5x − 4y = 21 and 3x + 5y = 20 →

Answer key

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

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