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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 32 · 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 + 7y = −40 and 7x + 2y = −5 →
  2. 2.6x + 3y = 21 and 3x + 2y = 8 →
  3. 3.6x + 4y = 38 and 2x − 5y = 0 →
  4. 4.2x − 4y = −10 and 4x + y = −11 →
  5. 5.3x + 6y = 51 and 6x + 3y = 30 →
  6. 6.5x + 3y = 48 and 3x + 5y = 48 →
  7. 7.5x − 6y = 58 and 4x + 3y = 23 →
  8. 8.2x − y = −21 and 6x + 5y = −39 →
  9. 9.5x + 5y = 35 and x − 5y = 1 →
  10. 10.8x + 4y = 60 and 4x + 8y = 84 →
  11. 11.9x + 2y = −6 and 2x + 9y = 50 →
  12. 12.2x − y = 21 and 4x + 3y = 7 →
  13. 13.x + 5y = −29 and 4x + 4y = −20 →
  14. 14.4x − y = 28 and x − 6y = −16 →
  15. 15.2x + 3y = 37 and 5x + 2y = 43 →
  16. 16.9x + 4y = −25 and 4x + 9y = 25 →
  17. 17.3x + 2y = 18 and 3x − 5y = −24 →
  18. 18.6x + 2y = 26 and 2x − 3y = −17 →
  19. 19.6x + y = 47 and 4x + 5y = 53 →
  20. 20.3x − 3y = 9 and 6x + 2y = −30 →
  21. 21.x + 3y = −24 and 2x + 2y = −12 →
  22. 22.4x − 3y = 10 and x + 4y = −26 →
  23. 23.5x + y = 23 and x + 5y = −5 →
  24. 24.x − 2y = −2 and 6x + 4y = 36 →
  25. 25.6x − 6y = −18 and 3x + 5y = 55 →
  26. 26.5x + 3y = 18 and 3x + 3y = 12 →
  27. 27.2x − 3y = −19 and x + y = 8 →
  28. 28.9x + 8y = 3 and 8x + 9y = 14 →
  29. 29.4x + 7y = −3 and 7x + 4y = 3 →
  30. 30.5x + 2y = 21 and 3x + 3y = 18 →
  31. 31.x + 5y = 12 and 5x − y = 8 →
  32. 32.2x + 6y = 36 and x − y = −14 →
  33. 33.3x + 6y = 54 and 6x + 3y = 36 →
  34. 34.2x + 2y = 8 and 3x + 5y = 14 →
  35. 35.5x + 4y = −19 and 2x + 2y = −8 →
  36. 36.x + 3y = 10 and 3x + y = 22 →
  37. 37.2x + 8y = 22 and 8x + 2y = −2 →
  38. 38.4x + 4y = −36 and 6x − 4y = −4 →
  39. 39.x + 8y = 20 and 8x + y = 34 →
  40. 40.x − 2y = 27 and 2x + 3y = −9 →

Answer key

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

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