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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 543 · 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 = −2 and 4x + y = −4 →
  2. 2.5x + 4y = 14 and 6x − 4y = 8 →
  3. 3.8x + 5y = 69 and 5x + 8y = 48 →
  4. 4.6x + 2y = 46 and 2x + 6y = 42 →
  5. 5.4x + 3y = −4 and x + 6y = 20 →
  6. 6.9x + 2y = 73 and 2x + 9y = 59 →
  7. 7.x − y = 2 and 2x − y = 10 →
  8. 8.7x + 8y = 54 and 8x + 7y = 51 →
  9. 9.5x + 3y = −29 and 3x + 5y = −11 →
  10. 10.6x + y = 57 and 2x + y = 21 →
  11. 11.2x + y = −3 and 5x − y = −32 →
  12. 12.8x + 6y = 86 and 6x + 8y = 96 →
  13. 13.x + 5y = 31 and x + y = 11 →
  14. 14.4x + 3y = 47 and 3x + 4y = 44 →
  15. 15.x − 6y = 35 and 3x − y = 20 →
  16. 16.3x + 4y = 25 and 4x + 3y = 17 →
  17. 17.x + 6y = −43 and 5x + 5y = −65 →
  18. 18.2x + 6y = 34 and 6x + 2y = 6 →
  19. 19.6x − y = 11 and 3x − 5y = −26 →
  20. 20.2x + 5y = −22 and 3x − 4y = −10 →
  21. 21.2x − 5y = −46 and x − 6y = −51 →
  22. 22.2x − 6y = −36 and 3x − 2y = 9 →
  23. 23.3x − y = 2 and 6x + 3y = 9 →
  24. 24.4x + 5y = 4 and 5x + 4y = −4 →
  25. 25.3x + 6y = 27 and 6x + 3y = 45 →
  26. 26.x + 3y = 9 and 3x + y = −21 →
  27. 27.3x + 3y = −51 and 2x + y = −25 →
  28. 28.3x + 3y = −12 and 6x + 2y = 0 →
  29. 29.4x + y = 36 and x + 4y = 24 →
  30. 30.4x + 3y = 23 and x + 2y = 12 →
  31. 31.2x + 7y = 31 and 7x + 2y = −4 →
  32. 32.4x + y = 18 and x + 4y = 27 →
  33. 33.x + 8y = −26 and 8x + y = 44 →
  34. 34.2x + y = −9 and x + 2y = 0 →
  35. 35.4x + 7y = −29 and 7x + 4y = 7 →
  36. 36.x − 6y = −3 and x + 4y = 7 →
  37. 37.3x + y = −13 and 4x + 2y = −20 →
  38. 38.x − 3y = 1 and 5x + 3y = −31 →
  39. 39.5x + 7y = 38 and 7x + 5y = 34 →
  40. 40.7x + 5y = 18 and 5x + 7y = 30 →

Answer key

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

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