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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 909 · 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 + 4y = 32 and 2x − 3y = −13 →
  2. 2.x + 3y = 20 and 3x + y = 12 →
  3. 3.x + 2y = 13 and 2x + y = 8 →
  4. 4.x + y = 10 and 2x + 4y = 28 →
  5. 5.3x − 4y = −27 and 6x + 6y = 30 →
  6. 6.6x − 4y = −52 and 5x + 6y = −34 →
  7. 7.4x − 4y = 24 and 2x − 3y = 10 →
  8. 8.x + 9y = 85 and 9x + y = 45 →
  9. 9.6x + 6y = −12 and 3x − 3y = 18 →
  10. 10.x − 6y = 40 and x + 6y = −32 →
  11. 11.6x − 4y = 78 and 2x + y = 12 →
  12. 12.3x + y = −14 and 6x + 3y = −30 →
  13. 13.8x + 3y = −51 and 3x + 8y = 29 →
  14. 14.5x − 5y = 35 and 2x − 6y = 18 →
  15. 15.x + 5y = −14 and 2x + 5y = −13 →
  16. 16.2x + 3y = 21 and 3x + 2y = 19 →
  17. 17.6x + 4y = −50 and x + 2y = −11 →
  18. 18.9x + 5y = −19 and 5x + 9y = −23 →
  19. 19.6x + y = 37 and 4x + 6y = 62 →
  20. 20.2x − 2y = 20 and 4x + y = 25 →
  21. 21.3x + 7y = 41 and 7x + 3y = 29 →
  22. 22.8x + 4y = 64 and 4x + 8y = 68 →
  23. 23.3x + y = 1 and x + 3y = −21 →
  24. 24.5x − 2y = 36 and 2x + y = 18 →
  25. 25.3x + 2y = 22 and 2x + 3y = 18 →
  26. 26.3x + 5y = 37 and 4x + 4y = 28 →
  27. 27.3x + 6y = 3 and x − 5y = 8 →
  28. 28.5x + 4y = −73 and 3x + 4y = −55 →
  29. 29.8x + y = 15 and x + 8y = −6 →
  30. 30.5x − 6y = −9 and 5x − 3y = 18 →
  31. 31.5x + 3y = −33 and 3x + 5y = −23 →
  32. 32.3x − 5y = −2 and x − 5y = −4 →
  33. 33.5x + 6y = −39 and 4x − 3y = 39 →
  34. 34.6x − 6y = −30 and 2x − 4y = −24 →
  35. 35.5x − 3y = −49 and x + 5y = 7 →
  36. 36.6x − 6y = 72 and 3x + 6y = −27 →
  37. 37.6x + y = 43 and x + 6y = 48 →
  38. 38.4x + 6y = 42 and x + 5y = 21 →
  39. 39.3x − 3y = −3 and 5x + 5y = −55 →
  40. 40.2x + 4y = 28 and 2x + 2y = 16 →

Answer key

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

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