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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 922 · 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 − 5y = −10 and x − 2y = −8 →
  2. 2.x − 3y = −23 and 4x + 4y = −12 →
  3. 3.6x + y = 57 and x + 6y = 27 →
  4. 4.5x + 4y = −21 and 6x + 4y = −26 →
  5. 5.x − 4y = 6 and 2x + 2y = 2 →
  6. 6.6x + 3y = −21 and 3x − 2y = −42 →
  7. 7.7x + 5y = 2 and 5x + 7y = −2 →
  8. 8.2x + 5y = −2 and 4x + 2y = 28 →
  9. 9.5x + 6y = 58 and 6x + 5y = 63 →
  10. 10.5x − y = 21 and 5x + y = 29 →
  11. 11.x + y = −8 and 3x + 5y = −22 →
  12. 12.5x + 4y = −15 and 4x + 5y = −21 →
  13. 13.2x − y = −14 and 3x + 5y = 5 →
  14. 14.6x + 5y = −60 and 3x + 3y = −33 →
  15. 15.8x + 3y = −5 and 3x + 8y = 5 →
  16. 16.5x − 5y = 50 and 4x + y = 10 →
  17. 17.3x − 2y = 32 and x + 2y = −8 →
  18. 18.3x + y = 13 and x + 4y = 30 →
  19. 19.2x − y = −18 and 5x + 3y = −23 →
  20. 20.2x + 2y = 14 and 4x − 2y = 22 →
  21. 21.5x + y = 41 and 2x − 5y = −16 →
  22. 22.4x − y = −7 and 2x + 6y = 16 →
  23. 23.x − y = 1 and x + 4y = 41 →
  24. 24.x + 3y = 16 and 4x + 2y = 24 →
  25. 25.2x + 4y = 20 and 5x + 2y = 18 →
  26. 26.3x − 6y = −63 and 5x + 4y = −21 →
  27. 27.6x − 3y = −6 and 2x + 4y = 38 →
  28. 28.2x + 6y = −34 and 6x + 2y = −6 →
  29. 29.2x + 3y = −11 and 4x + 4y = −12 →
  30. 30.6x + 3y = 30 and x + 6y = −17 →
  31. 31.5x + 2y = −46 and x + 3y = −17 →
  32. 32.9x + 6y = 45 and 6x + 9y = 60 →
  33. 33.5x − 6y = −21 and 4x − 5y = −17 →
  34. 34.6x − 2y = 6 and x + 6y = 20 →
  35. 35.8x + 4y = 80 and 4x + 8y = 76 →
  36. 36.4x + 2y = 46 and 5x + 4y = 68 →
  37. 37.6x + 3y = 18 and 3x + 6y = −18 →
  38. 38.6x + y = 19 and x + y = −1 →
  39. 39.3x − 4y = −20 and x − 2y = −12 →
  40. 40.2x + 5y = −36 and 5x + 2y = −48 →

Answer key

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

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