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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 449 · 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 − 3y = 0 and 6x − 6y = 12 →
  2. 2.2x + 2y = 6 and 6x − 2y = 26 →
  3. 3.4x − 4y = 20 and 4x − 2y = 4 →
  4. 4.8x + 5y = −18 and 5x + 8y = 18 →
  5. 5.2x + 8y = −18 and 8x + 2y = 18 →
  6. 6.3x + 3y = −18 and 4x − 6y = 46 →
  7. 7.3x + 9y = 72 and 9x + 3y = 72 →
  8. 8.x + 6y = 18 and 5x − y = −34 →
  9. 9.3x + 3y = 21 and 4x − 4y = −20 →
  10. 10.4x − 5y = −71 and 2x − 6y = −60 →
  11. 11.5x + 7y = 28 and 7x + 5y = 44 →
  12. 12.x + 7y = −36 and 7x + y = −60 →
  13. 13.5x + y = 1 and x + 6y = −52 →
  14. 14.5x + 4y = −29 and 4x + 5y = −16 →
  15. 15.6x + y = −40 and x + 6y = 40 →
  16. 16.x − 3y = 19 and 6x − y = 46 →
  17. 17.3x + 2y = 1 and 6x + y = 14 →
  18. 18.2x + 5y = 46 and 6x + 5y = 58 →
  19. 19.5x + 3y = 28 and 4x − 5y = 52 →
  20. 20.3x + 3y = −3 and 2x + 4y = −14 →
  21. 21.5x + 2y = −19 and 2x − 4y = 26 →
  22. 22.4x + 2y = 50 and 2x + 4y = 52 →
  23. 23.2x + 5y = 47 and 5x + y = 37 →
  24. 24.6x − y = −15 and 2x + 6y = 14 →
  25. 25.2x + y = 16 and 3x + 5y = 17 →
  26. 26.5x + 6y = −16 and 6x + 5y = −6 →
  27. 27.x + 6y = 23 and 4x + 6y = 2 →
  28. 28.x + 4y = 7 and 4x + y = −32 →
  29. 29.6x + 6y = −54 and 2x + 5y = −36 →
  30. 30.9x + 7y = −73 and 7x + 9y = −71 →
  31. 31.3x + y = −10 and x + 3y = −14 →
  32. 32.6x − 5y = −46 and 6x + 4y = −28 →
  33. 33.7x + 8y = 50 and 8x + 7y = 40 →
  34. 34.6x + 7y = 46 and 7x + 6y = 45 →
  35. 35.5x + 2y = 13 and 6x + 6y = 30 →
  36. 36.2x − 6y = 30 and 3x + 3y = 21 →
  37. 37.3x + 5y = −39 and 5x + 3y = −33 →
  38. 38.6x + 8y = −32 and 8x + 6y = −38 →
  39. 39.x + 2y = 3 and 2x − 2y = −18 →
  40. 40.3x + 7y = −24 and 7x + 3y = −16 →

Answer key

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

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