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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 97 · 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. 1.6x − 2y = −14 and 3x + y = −17 →
  2. 2.3x − 4y = −63 and 5x + 2y = −27 →
  3. 3.3x + y = 11 and x + 3y = −15 →
  4. 4.3x + 9y = 36 and 9x + 3y = 84 →
  5. 5.2x + 4y = 42 and 3x − 2y = 7 →
  6. 6.8x + 4y = −4 and 4x + 8y = 52 →
  7. 7.4x + 8y = 0 and 8x + 4y = −48 →
  8. 8.3x + 6y = 42 and 6x + 3y = 30 →
  9. 9.5x + 6y = 37 and 6x + 3y = 36 →
  10. 10.x + 2y = −7 and 2x + y = −11 →
  11. 11.9x + 6y = 51 and 6x + 9y = 9 →
  12. 12.6x + y = 21 and 5x + 2y = 28 →
  13. 13.x + 3y = −8 and 2x + y = −1 →
  14. 14.3x + 6y = −30 and 6x + 3y = 21 →
  15. 15.4x + y = 45 and x + 5y = 54 →
  16. 16.4x + 2y = 12 and 4x + 3y = 20 →
  17. 17.6x + 7y = −1 and 7x + 6y = 1 →
  18. 18.6x + 5y = 51 and 5x + 6y = 59 →
  19. 19.4x + 3y = −13 and 3x − 5y = 12 →
  20. 20.x + 5y = 7 and 5x + y = −13 →
  21. 21.9x + 6y = −6 and 6x + 9y = 36 →
  22. 22.4x − 3y = 23 and 4x + 4y = −12 →
  23. 23.2x − 3y = 30 and x + 2y = −6 →
  24. 24.6x + 5y = 23 and 6x + 2y = 20 →
  25. 25.6x − 5y = 1 and 2x + 6y = 8 →
  26. 26.5x − 4y = 33 and 5x + 6y = 63 →
  27. 27.6x + 2y = 14 and 2x + 6y = −22 →
  28. 28.3x + 4y = 19 and 4x + 3y = 23 →
  29. 29.5x + y = −34 and 6x − 3y = −45 →
  30. 30.4x − 2y = −38 and 4x + 3y = −33 →
  31. 31.3x + 2y = 12 and 6x + 2y = 30 →
  32. 32.x + 6y = 3 and 6x + y = −17 →
  33. 33.2x + 2y = 24 and 6x + 2y = 36 →
  34. 34.5x + 2y = 26 and x − 5y = −38 →
  35. 35.3x − y = 16 and 4x + 6y = 80 →
  36. 36.3x + y = −24 and 3x − y = −6 →
  37. 37.2x + 5y = 16 and 6x − 3y = 12 →
  38. 38.5x + y = 45 and 4x + 3y = 47 →
  39. 39.5x + 4y = −22 and 3x + y = −2 →
  40. 40.4x + 6y = −86 and 5x − 4y = −4 →

Answer key

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

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