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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 696 · 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. 1.5x + 4y = −26 and 3x − 3y = −21 →
  2. 2.2x + 9y = −6 and 9x + 2y = 50 →
  3. 3.5x + y = 42 and x − 2y = −7 →
  4. 4.7x + 6y = 16 and 6x + 7y = 23 →
  5. 5.4x − 3y = 5 and 2x + 5y = 61 →
  6. 6.3x + 6y = 39 and x − 6y = −3 →
  7. 7.5x + 3y = −3 and 2x + y = 0 →
  8. 8.4x + 3y = −17 and x + y = −4 →
  9. 9.4x + y = 25 and 3x + 3y = 12 →
  10. 10.5x + 2y = 33 and 6x − 2y = 22 →
  11. 11.x + 5y = 0 and 3x − 5y = 20 →
  12. 12.4x + 3y = −12 and x − 3y = −18 →
  13. 13.6x − 4y = 44 and 5x − 2y = 34 →
  14. 14.x + 5y = 22 and 5x + y = 14 →
  15. 15.3x + 6y = 27 and 6x + 3y = −27 →
  16. 16.7x + 2y = 23 and 2x + 7y = 58 →
  17. 17.2x − 2y = −10 and 3x + 2y = 15 →
  18. 18.2x + 5y = −27 and 5x − 3y = 72 →
  19. 19.3x + y = −26 and 2x + 4y = −14 →
  20. 20.5x + y = −22 and x + 5y = 34 →
  21. 21.6x + 6y = −24 and 5x + y = 0 →
  22. 22.2x + 3y = 19 and 3x + 4y = 26 →
  23. 23.x + 2y = 19 and 3x + 2y = 29 →
  24. 24.4x − 6y = 56 and 3x + 2y = 3 →
  25. 25.6x + 4y = 46 and 3x + 3y = 21 →
  26. 26.2x + 5y = 28 and 2x + 2y = 22 →
  27. 27.6x + 5y = −9 and 2x + 2y = −6 →
  28. 28.3x + 5y = 16 and x − 3y = −4 →
  29. 29.2x + 8y = 28 and 8x + 2y = 22 →
  30. 30.2x − 5y = −24 and 5x + 5y = 45 →
  31. 31.3x + 3y = 6 and 2x − 3y = −16 →
  32. 32.6x + y = 23 and x − 6y = 10 →
  33. 33.3x − 5y = 16 and x − 2y = 5 →
  34. 34.x + 5y = −14 and 3x + 5y = −2 →
  35. 35.8x + 6y = −46 and 6x + 8y = −66 →
  36. 36.4x + 2y = 38 and 2x + 4y = 28 →
  37. 37.6x + 9y = 51 and 9x + 6y = 69 →
  38. 38.4x + 2y = 22 and 4x + 4y = 8 →
  39. 39.4x + 4y = −16 and x − 5y = 38 →
  40. 40.2x + y = −10 and x + 2y = −8 →

Answer key

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

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