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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 583 · 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 + 3y = −1 and 2x − 4y = −8 →
  2. 2.8x + 3y = 49 and 3x + 8y = −16 →
  3. 3.4x + 5y = 19 and 4x − y = 25 →
  4. 4.4x − 4y = 28 and x + 3y = −5 →
  5. 5.4x − 6y = 6 and x + 4y = 7 →
  6. 6.x − 4y = −12 and 5x + 4y = −36 →
  7. 7.6x − 6y = −18 and 2x + 4y = −24 →
  8. 8.2x + 6y = 12 and 6x + 2y = 52 →
  9. 9.5x + y = 44 and 4x + y = 35 →
  10. 10.5x + y = 16 and 4x + 6y = −34 →
  11. 11.8x + y = 81 and x + 8y = 81 →
  12. 12.2x + 2y = 4 and 4x + 2y = 20 →
  13. 13.4x + 5y = 53 and 5x + 4y = 46 →
  14. 14.x + 6y = 58 and 5x + 2y = 38 →
  15. 15.3x − 3y = −27 and 2x + 2y = 6 →
  16. 16.5x + 2y = 1 and 6x + 6y = 12 →
  17. 17.4x − 6y = −10 and 5x + 4y = 45 →
  18. 18.3x − 6y = −27 and 4x + 3y = 30 →
  19. 19.9x + 5y = 51 and 5x + 9y = 47 →
  20. 20.2x − y = 2 and 2x + 2y = 20 →
  21. 21.x + 5y = 18 and 5x − y = −40 →
  22. 22.x + 6y = 27 and 3x + y = 13 →
  23. 23.8x + 9y = 23 and 9x + 8y = 28 →
  24. 24.5x + 4y = 3 and 4x + 5y = −12 →
  25. 25.5x − 6y = −44 and 6x + 2y = 30 →
  26. 26.3x − 3y = −33 and 3x − 2y = −31 →
  27. 27.8x + 5y = 7 and 5x + 8y = 19 →
  28. 28.4x + 8y = 20 and 8x + 4y = 28 →
  29. 29.x + 3y = −13 and x + 4y = −18 →
  30. 30.5x + y = 19 and x + 5y = −1 →
  31. 31.9x + 5y = 42 and 5x + 9y = −14 →
  32. 32.2x − 5y = 48 and 5x + 5y = 15 →
  33. 33.6x + 2y = 16 and 4x + y = 10 →
  34. 34.6x + 3y = 54 and 3x + 6y = 54 →
  35. 35.2x − 4y = −26 and 6x + 2y = −36 →
  36. 36.4x + 3y = −31 and 2x + 4y = −18 →
  37. 37.x + y = 5 and 2x − 4y = 22 →
  38. 38.x + 2y = −14 and 2x + y = −4 →
  39. 39.4x + y = −38 and 6x + 3y = −66 →
  40. 40.4x − 5y = 11 and 3x + 6y = 57 →

Answer key

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

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