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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 783 · 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. 1.5x + 4y = 11 and 4x + 5y = −2 →
  2. 2.2x − 2y = −8 and 6x − 4y = −12 →
  3. 3.5x + y = −16 and x + 5y = 16 →
  4. 4.x + 4y = 19 and 4x + 6y = 46 →
  5. 5.4x + 7y = 60 and 7x + 4y = 72 →
  6. 6.x + 3y = −12 and 5x − y = 20 →
  7. 7.x − 3y = −18 and 5x + 2y = −39 →
  8. 8.4x + 4y = 24 and 4x + 3y = 23 →
  9. 9.2x + 4y = 40 and 3x − 3y = −3 →
  10. 10.x − 4y = 28 and 3x − 3y = 39 →
  11. 11.7x + 4y = 25 and 4x + 7y = −14 →
  12. 12.4x + 4y = 24 and 6x + 2y = 44 →
  13. 13.8x + 6y = 58 and 6x + 8y = 54 →
  14. 14.4x + 3y = −5 and 2x − 6y = −10 →
  15. 15.3x − 3y = −12 and 2x + 4y = 22 →
  16. 16.x + 2y = 13 and 3x + 3y = 15 →
  17. 17.7x + 3y = −83 and 3x + 7y = −87 →
  18. 18.5x + 9y = 72 and 9x + 5y = 96 →
  19. 19.3x − y = −12 and 2x − 6y = 24 →
  20. 20.x + 3y = 19 and 6x + 6y = 54 →
  21. 21.8x + 9y = −7 and 9x + 8y = −10 →
  22. 22.5x − y = 30 and 5x − 6y = 5 →
  23. 23.2x + 3y = 15 and 6x + 3y = 39 →
  24. 24.5x + 2y = −4 and 3x + 2y = 0 →
  25. 25.3x + 6y = 48 and 4x + 3y = 44 →
  26. 26.x + 6y = −2 and 3x − 2y = 14 →
  27. 27.6x + 3y = 69 and 2x − y = 5 →
  28. 28.x + 3y = 15 and 4x + 6y = 48 →
  29. 29.3x − 2y = 13 and 5x + 2y = 43 →
  30. 30.x + 6y = 63 and 4x + 2y = 54 →
  31. 31.5x − 5y = −15 and 2x + 5y = 57 →
  32. 32.6x + 4y = 56 and 5x − 2y = 20 →
  33. 33.5x − 5y = 0 and 6x − y = 25 →
  34. 34.2x + 6y = −10 and 4x + 4y = −28 →
  35. 35.x + 6y = −6 and 3x + 4y = 10 →
  36. 36.5x − 2y = 7 and x + 3y = −2 →
  37. 37.3x + 7y = −34 and 7x + 3y = 14 →
  38. 38.6x + 7y = 5 and 7x + 6y = −5 →
  39. 39.5x + 2y = −29 and x − 3y = −16 →
  40. 40.5x + 6y = 28 and 2x + y = 0 →

Answer key

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

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