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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 88 · 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.x + 6y = 17 and 5x + 2y = −27 →
  2. 2.4x + 5y = −2 and x + 3y = 10 →
  3. 3.3x + 4y = 11 and 4x + y = −20 →
  4. 4.2x − 6y = 56 and x + 3y = −20 →
  5. 5.6x − 2y = −32 and x + 4y = −1 →
  6. 6.x + y = −6 and 2x + 3y = −20 →
  7. 7.3x − y = −7 and 6x − 3y = −15 →
  8. 8.5x + y = −48 and x + 4y = −40 →
  9. 9.6x + 3y = 27 and 3x + 6y = 18 →
  10. 10.6x − y = 12 and 3x + y = −3 →
  11. 11.3x + 5y = −8 and 5x + 3y = −8 →
  12. 12.x + 2y = −1 and 6x + 3y = 3 →
  13. 13.2x + 6y = 48 and 4x + 3y = 33 →
  14. 14.x − 6y = −10 and 6x + 3y = 18 →
  15. 15.6x + 2y = 48 and 3x − 6y = 3 →
  16. 16.4x + 3y = 22 and 3x + 2y = 15 →
  17. 17.x + 8y = 27 and 8x + y = 27 →
  18. 18.4x + 3y = 42 and 4x − 3y = 6 →
  19. 19.3x − 4y = −8 and 3x − 6y = −24 →
  20. 20.2x + 3y = −22 and 5x + 2y = −11 →
  21. 21.5x + y = −2 and x + 5y = 14 →
  22. 22.2x + 4y = 16 and 4x − y = 23 →
  23. 23.5x + 4y = −46 and 4x + y = −28 →
  24. 24.3x − y = −22 and 3x + 2y = −28 →
  25. 25.3x + 5y = 26 and 5x + 3y = 6 →
  26. 26.x − 2y = −10 and 3x − 4y = −14 →
  27. 27.4x + 8y = 44 and 8x + 4y = −8 →
  28. 28.4x + 3y = −26 and 3x − 2y = −28 →
  29. 29.3x + 6y = −15 and 4x − 4y = −44 →
  30. 30.7x + 3y = 39 and 3x + 7y = 51 →
  31. 31.4x + 3y = 47 and 6x + 3y = 63 →
  32. 32.5x + 8y = 52 and 8x + 5y = 52 →
  33. 33.4x + 4y = −4 and 3x − 6y = −21 →
  34. 34.x + 7y = 66 and 7x + y = 30 →
  35. 35.2x + 2y = 12 and 4x + 2y = 20 →
  36. 36.4x − 5y = 52 and x − 2y = 19 →
  37. 37.5x + 4y = 27 and 5x + 6y = 43 →
  38. 38.9x + 7y = 79 and 7x + 9y = 65 →
  39. 39.6x + 5y = 33 and 2x + 2y = 12 →
  40. 40.x + 5y = −22 and x + 2y = −4 →

Answer key

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

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