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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 155 · 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. 1.2x + 6y = 38 and 5x + 3y = −13 →
  2. 2.3x + 5y = 3 and 2x + 5y = 7 →
  3. 3.2x + 6y = 20 and 6x + 2y = −36 →
  4. 4.3x − 3y = −12 and 4x − 3y = −13 →
  5. 5.8x + 3y = 39 and 3x + 8y = 49 →
  6. 6.5x + 3y = 19 and 5x + 2y = 21 →
  7. 7.3x − 2y = −18 and 2x + 2y = −2 →
  8. 8.3x − y = 7 and 5x + 4y = 40 →
  9. 9.x + 4y = 41 and 4x + y = 44 →
  10. 10.7x + y = 6 and x + 7y = −54 →
  11. 11.9x + 6y = 51 and 6x + 9y = 24 →
  12. 12.3x + 3y = −6 and 2x + 5y = 17 →
  13. 13.2x + 4y = 8 and 2x − 4y = 0 →
  14. 14.6x − y = 17 and 5x + y = 27 →
  15. 15.2x − 6y = −14 and 5x − 6y = −17 →
  16. 16.4x − 5y = 3 and 2x + 2y = −30 →
  17. 17.5x + 3y = 36 and 3x + 5y = 12 →
  18. 18.6x + 5y = −61 and 5x + 6y = −60 →
  19. 19.3x + 2y = 10 and 2x + y = 9 →
  20. 20.6x + 7y = −99 and 7x + 6y = −96 →
  21. 21.3x − 6y = 42 and 2x + y = −17 →
  22. 22.7x + 3y = 29 and 3x + 7y = 41 →
  23. 23.5x + 3y = −29 and 2x + 2y = −10 →
  24. 24.7x + 5y = 68 and 5x + 7y = 76 →
  25. 25.4x − 4y = 20 and 4x − y = 32 →
  26. 26.9x + 5y = 48 and 5x + 9y = 64 →
  27. 27.3x − y = −3 and 2x + 2y = 22 →
  28. 28.x + 8y = 19 and 8x + y = −37 →
  29. 29.4x + y = −9 and x + 4y = 9 →
  30. 30.4x + 7y = 23 and 7x + 4y = −1 →
  31. 31.8x + y = −52 and x + 8y = −38 →
  32. 32.6x − y = 41 and 4x + 4y = 60 →
  33. 33.4x + 5y = −1 and 5x + 4y = 10 →
  34. 34.4x + 5y = 33 and 4x + 6y = 34 →
  35. 35.8x + 7y = 16 and 7x + 8y = −1 →
  36. 36.4x + 3y = −10 and x + 4y = 17 →
  37. 37.3x + 2y = 12 and 4x + y = 11 →
  38. 38.2x + y = 15 and 2x + 6y = 10 →
  39. 39.3x + 2y = 1 and 2x + 2y = −2 →
  40. 40.3x + 2y = −13 and 2x − 4y = −46 →

Answer key

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

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