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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 50 · 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.x + 9y = −26 and 9x + y = 6 →
  2. 2.x + y = 4 and 5x + 6y = 16 →
  3. 3.4x + 6y = 76 and 6x + 4y = 74 →
  4. 4.6x + 3y = 63 and 4x + 6y = 78 →
  5. 5.2x + 4y = 18 and 4x + 2y = 30 →
  6. 6.4x + y = −6 and x + 4y = 21 →
  7. 7.3x + y = −5 and 4x − 2y = −10 →
  8. 8.3x + 3y = 39 and 5x + 4y = 57 →
  9. 9.4x + y = −17 and 3x + 5y = −34 →
  10. 10.3x + 4y = −3 and 3x − y = 12 →
  11. 11.6x + y = 42 and x + 6y = 42 →
  12. 12.3x − 4y = 2 and 2x + 6y = 36 →
  13. 13.6x − y = −23 and 3x − y = −14 →
  14. 14.2x + 2y = −2 and x + 2y = 4 →
  15. 15.5x + 2y = 18 and 5x + 6y = −6 →
  16. 16.3x + 6y = 57 and 5x + 5y = 50 →
  17. 17.2x + y = 11 and 2x + 4y = 8 →
  18. 18.8x + 5y = 46 and 5x + 8y = 58 →
  19. 19.5x − 5y = 0 and 2x + 6y = 16 →
  20. 20.2x − 5y = 21 and 4x + 6y = −6 →
  21. 21.6x + 4y = 22 and x + 5y = 21 →
  22. 22.x + 3y = −7 and 3x + y = −13 →
  23. 23.4x + 5y = 8 and 3x − 4y = −25 →
  24. 24.9x + 4y = 91 and 4x + 9y = 91 →
  25. 25.5x + 7y = 4 and 7x + 5y = −4 →
  26. 26.2x + 8y = 28 and 8x + 2y = −8 →
  27. 27.5x + 9y = 91 and 9x + 5y = 63 →
  28. 28.x + 5y = 41 and 5x + y = 37 →
  29. 29.9x + 5y = 71 and 5x + 9y = 83 →
  30. 30.2x + 6y = −10 and 3x + 4y = −5 →
  31. 31.3x + 9y = −21 and 9x + 3y = 57 →
  32. 32.4x − 4y = 8 and x + 6y = 16 →
  33. 33.3x + 3y = −48 and 2x + 5y = −53 →
  34. 34.6x + 4y = −58 and 4x + 2y = −38 →
  35. 35.x + 3y = −13 and 3x + y = −23 →
  36. 36.x − 3y = 0 and 4x − 3y = 9 →
  37. 37.x − 4y = −14 and 3x − 2y = −22 →
  38. 38.3x + 2y = 10 and 2x + 3y = 20 →
  39. 39.6x + 4y = 0 and 4x + 6y = 20 →
  40. 40.3x + y = 13 and x + 3y = 23 →

Answer key

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

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