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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 134 · 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. 1.8x + 3y = 46 and 3x + 8y = 31 →
  2. 2.4x + 2y = 14 and 3x + 4y = 23 →
  3. 3.5x + 2y = −26 and 2x + 5y = −44 →
  4. 4.2x + 5y = 29 and 6x + y = 17 →
  5. 5.6x + 2y = 36 and 4x + 4y = 48 →
  6. 6.8x + 2y = −46 and 2x + 8y = 26 →
  7. 7.2x + 4y = 36 and 3x + 3y = 36 →
  8. 8.6x + y = 4 and x + 6y = −11 →
  9. 9.5x + 2y = 41 and 5x + 6y = 73 →
  10. 10.x − 2y = 11 and 6x − 2y = 56 →
  11. 11.x + 9y = −30 and 9x + y = 50 →
  12. 12.x + y = 5 and 6x + 5y = 28 →
  13. 13.5x + y = 30 and 5x − 5y = 0 →
  14. 14.x + 3y = 3 and x + 2y = 4 →
  15. 15.2x + 2y = 24 and 5x + 3y = 50 →
  16. 16.2x + 3y = −12 and 4x + 2y = −16 →
  17. 17.x + 4y = −20 and x + y = −11 →
  18. 18.2x + 8y = 28 and 8x + 2y = −8 →
  19. 19.8x + 6y = −10 and 6x + 8y = −4 →
  20. 20.8x + 7y = 88 and 7x + 8y = 92 →
  21. 21.3x + 5y = 2 and 3x − 6y = 24 →
  22. 22.3x + 4y = −13 and x + 2y = −3 →
  23. 23.4x + 3y = 15 and 4x + 6y = 6 →
  24. 24.6x + y = −55 and 4x + 6y = −74 →
  25. 25.x + 5y = 7 and 4x + 4y = 12 →
  26. 26.x + 3y = −10 and 3x + y = 2 →
  27. 27.4x + 6y = 62 and 6x + 5y = 57 →
  28. 28.4x + y = 23 and 3x − 5y = 69 →
  29. 29.4x − 4y = −48 and 6x + y = −16 →
  30. 30.3x + 3y = 33 and 5x + 6y = 60 →
  31. 31.x + 5y = 4 and 2x − y = −14 →
  32. 32.5x + y = −38 and x + 5y = 26 →
  33. 33.4x + 3y = 63 and 3x + 4y = 63 →
  34. 34.7x + y = −40 and x + 7y = 56 →
  35. 35.x + 6y = −34 and 6x + y = 41 →
  36. 36.3x + 9y = 30 and 9x + 3y = 18 →
  37. 37.4x + 9y = 30 and 9x + 4y = 35 →
  38. 38.7x + 6y = 6 and 6x + 7y = 20 →
  39. 39.2x + 4y = 6 and 4x + 2y = −18 →
  40. 40.9x + 8y = 55 and 8x + 9y = 64 →

Answer key

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

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