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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 65 · 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 = 26 and 3x + 6y = 6 →
  2. 2.6x + 3y = 9 and 2x + 6y = −42 →
  3. 3.2x + 5y = 43 and 6x + 4y = 74 →
  4. 4.6x + y = −23 and 6x − 4y = −28 →
  5. 5.3x − 5y = −34 and 4x + 2y = 24 →
  6. 6.x + 4y = 22 and 3x + 5y = 17 →
  7. 7.2x + 8y = 52 and 8x + 2y = 58 →
  8. 8.6x + 9y = 27 and 9x + 6y = −27 →
  9. 9.2x + 2y = 10 and 3x + y = 9 →
  10. 10.3x + 4y = −8 and 6x + 5y = −19 →
  11. 11.x + 3y = 19 and 3x + y = 1 →
  12. 12.4x − 4y = −24 and 5x + 5y = −10 →
  13. 13.5x + 2y = −14 and 2x + 5y = 28 →
  14. 14.x − y = −1 and 5x + 4y = 13 →
  15. 15.6x + 4y = 60 and 4x + 6y = 50 →
  16. 16.x + 6y = −6 and 4x + 2y = 20 →
  17. 17.x + 2y = −9 and 5x + 6y = −13 →
  18. 18.5x − y = −8 and 2x + 4y = 10 →
  19. 19.8x + 7y = −31 and 7x + 8y = −44 →
  20. 20.x + 5y = −25 and x − 5y = 15 →
  21. 21.3x + 2y = −3 and x − 4y = 41 →
  22. 22.x + 2y = 27 and 2x + y = 27 →
  23. 23.3x − 6y = 45 and 3x + 3y = 9 →
  24. 24.4x + 7y = −22 and 7x + 4y = −55 →
  25. 25.3x + y = 24 and 2x − 4y = −26 →
  26. 26.4x − 2y = −2 and 3x + 4y = 48 →
  27. 27.5x + y = −34 and x + 3y = −4 →
  28. 28.2x − 6y = −2 and 6x + 2y = 54 →
  29. 29.5x + 4y = 7 and x + 5y = −28 →
  30. 30.9x + 2y = −63 and 2x + 9y = −91 →
  31. 31.4x + 3y = −7 and 3x + 4y = −21 →
  32. 32.5x + y = −30 and x − 2y = −17 →
  33. 33.x − 5y = −31 and 6x + 5y = 59 →
  34. 34.5x + 6y = −64 and x − y = −4 →
  35. 35.2x + y = 4 and x + 2y = 5 →
  36. 36.2x + 2y = −6 and x + 2y = −10 →
  37. 37.3x + 7y = −8 and 7x + 3y = 8 →
  38. 38.5x + 6y = 56 and x + y = 10 →
  39. 39.x − 4y = −2 and 4x + 5y = 34 →
  40. 40.4x + 5y = −25 and 5x + 4y = −29 →

Answer key

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

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