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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 403 · 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. 1.3x + 2y = 33 and x + 5y = 37 →
  2. 2.8x + 5y = −83 and 5x + 8y = −86 →
  3. 3.3x + y = 32 and x + 5y = 48 →
  4. 4.3x + 6y = −9 and 6x + 3y = 9 →
  5. 5.6x + 6y = 18 and 3x − 3y = −27 →
  6. 6.6x − 5y = 2 and 2x + y = 6 →
  7. 7.5x + y = 13 and 4x − 3y = 37 →
  8. 8.6x + 8y = 100 and 8x + 6y = 96 →
  9. 9.2x + 2y = 12 and 2x + 4y = 10 →
  10. 10.4x + y = 17 and 2x + 4y = 26 →
  11. 11.6x + 5y = −19 and 5x + 6y = −14 →
  12. 12.4x + 7y = −65 and 7x + 4y = −56 →
  13. 13.5x + 5y = 40 and 2x − 5y = −26 →
  14. 14.3x + 4y = 27 and 4x + 3y = 22 →
  15. 15.2x + 9y = −51 and 9x + 2y = −37 →
  16. 16.6x − 2y = −40 and 3x + 3y = −12 →
  17. 17.2x + 6y = 20 and 6x + 2y = 44 →
  18. 18.2x + y = 19 and 3x + 6y = 42 →
  19. 19.3x + 8y = 83 and 8x + 3y = 93 →
  20. 20.8x + 9y = 47 and 9x + 8y = 38 →
  21. 21.x + 4y = −17 and 4x + 4y = −8 →
  22. 22.2x + 6y = −14 and 6x + 2y = −10 →
  23. 23.5x + y = −24 and x + 5y = 0 →
  24. 24.x − 5y = 46 and 5x − 4y = 62 →
  25. 25.x + 9y = −4 and 9x + y = 44 →
  26. 26.2x + 5y = 20 and 6x − 6y = 18 →
  27. 27.3x − 5y = −4 and 5x − 6y = −16 →
  28. 28.4x − 2y = 2 and x + 5y = 28 →
  29. 29.4x − 3y = 0 and 4x − 4y = −4 →
  30. 30.3x − 4y = −13 and 6x + 3y = 18 →
  31. 31.5x + y = −44 and 3x − 4y = −31 →
  32. 32.5x + 2y = 28 and x + y = 8 →
  33. 33.6x − 2y = −52 and 6x − y = −53 →
  34. 34.x + y = 0 and 2x + y = 8 →
  35. 35.5x − 3y = −6 and 6x + 3y = −27 →
  36. 36.4x + 6y = 26 and 6x + 4y = 44 →
  37. 37.4x + y = 19 and x + 4y = 1 →
  38. 38.6x + 7y = 16 and 7x + 6y = 10 →
  39. 39.2x − 6y = −66 and 6x − 3y = −63 →
  40. 40.2x + 4y = 6 and 6x + y = −48 →

Answer key

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

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