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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 518 · 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 + 5y = −20 and 4x − 5y = −61 →
  2. 2.3x + y = 28 and x + 3y = 12 →
  3. 3.3x − 3y = 24 and x + 3y = 12 →
  4. 4.x + 5y = −19 and x − 2y = 9 →
  5. 5.3x + y = 22 and x + 3y = 2 →
  6. 6.x + 5y = 11 and 4x − y = 2 →
  7. 7.7x + 8y = −19 and 8x + 7y = −26 →
  8. 8.4x + 4y = 16 and 5x + 2y = −4 →
  9. 9.2x + 4y = 24 and 4x − 3y = −51 →
  10. 10.2x − 6y = 14 and x − 4y = 12 →
  11. 11.5x − 5y = −15 and 5x − y = 5 →
  12. 12.6x + 7y = −8 and 7x + 6y = −5 →
  13. 13.6x + 4y = 76 and 3x + 4y = 52 →
  14. 14.3x + 6y = 42 and 3x + 2y = 10 →
  15. 15.5x − 5y = 30 and 6x − y = 26 →
  16. 16.6x + 4y = 52 and 2x + y = 16 →
  17. 17.2x + 3y = −21 and 5x − y = −27 →
  18. 18.6x + 4y = 60 and 6x + y = 42 →
  19. 19.3x + 5y = 2 and 6x + 6y = 12 →
  20. 20.6x + 9y = 117 and 9x + 6y = 108 →
  21. 21.6x + 2y = 34 and 2x + 6y = 54 →
  22. 22.x − 3y = 8 and 3x + 6y = −36 →
  23. 23.2x − 3y = −14 and 4x + 5y = 38 →
  24. 24.2x + 2y = 6 and 5x + 3y = 25 →
  25. 25.5x + 7y = 11 and 7x + 5y = −23 →
  26. 26.5x + y = −18 and 3x + 5y = −2 →
  27. 27.4x + 5y = 39 and 5x + 4y = 42 →
  28. 28.3x − 3y = 39 and 6x + 3y = 42 →
  29. 29.6x − 5y = 4 and x − 6y = −20 →
  30. 30.3x + 6y = −30 and 2x + 3y = −13 →
  31. 31.6x + 7y = 90 and 7x + 6y = 92 →
  32. 32.6x + 8y = −46 and 8x + 6y = −66 →
  33. 33.2x − 2y = 14 and 2x + 3y = −16 →
  34. 34.x + 3y = −10 and x − y = −6 →
  35. 35.6x − 2y = −28 and 5x + y = −18 →
  36. 36.8x + 2y = 28 and 2x + 8y = −38 →
  37. 37.4x + 2y = 26 and 2x − 4y = 38 →
  38. 38.6x + 4y = 12 and 4x + 6y = 28 →
  39. 39.6x + 3y = 9 and 3x + 6y = 0 →
  40. 40.4x − 6y = −80 and 3x + 2y = −8 →

Answer key

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

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