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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 160 · 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. 1.4x − 2y = −8 and 3x + 3y = 30 →
  2. 2.3x + 8y = 11 and 8x + 3y = 66 →
  3. 3.x + 3y = 35 and 2x + y = 25 →
  4. 4.7x + 4y = 5 and 4x + 7y = 17 →
  5. 5.x + y = −13 and 3x + 6y = −54 →
  6. 6.3x − 5y = −31 and x + 2y = −3 →
  7. 7.2x + 5y = 19 and 2x + 6y = 20 →
  8. 8.2x − 3y = 9 and 2x + y = 5 →
  9. 9.9x + 7y = 84 and 7x + 9y = 76 →
  10. 10.5x + y = −36 and 6x + 5y = −9 →
  11. 11.7x + 9y = −26 and 9x + 7y = −38 →
  12. 12.6x + 5y = −17 and 2x + 6y = 16 →
  13. 13.x − y = −10 and 6x + 2y = −12 →
  14. 14.4x + y = −22 and 3x + y = −15 →
  15. 15.6x − 4y = −30 and 3x − y = −12 →
  16. 16.4x + 5y = 57 and 5x + 4y = 51 →
  17. 17.3x + 5y = −8 and 3x + 3y = 0 →
  18. 18.2x − 6y = −24 and x + 6y = 6 →
  19. 19.5x + 4y = −22 and 4x + 5y = −23 →
  20. 20.3x + 6y = 39 and x + 5y = 25 →
  21. 21.x − y = 6 and 3x + 4y = 32 →
  22. 22.4x + 3y = −37 and 4x + 6y = −46 →
  23. 23.6x − 2y = −58 and 6x + 6y = −42 →
  24. 24.9x + 3y = −3 and 3x + 9y = −57 →
  25. 25.x + 8y = 11 and 8x + y = −38 →
  26. 26.4x + 7y = 18 and 7x + 4y = 15 →
  27. 27.8x + 3y = −21 and 3x + 8y = 54 →
  28. 28.6x − 5y = −52 and 5x + 2y = 6 →
  29. 29.4x − 2y = −40 and 5x + 4y = −37 →
  30. 30.6x + y = 33 and 3x + y = 15 →
  31. 31.3x − 5y = 9 and 6x − 2y = 42 →
  32. 32.2x + 2y = 2 and 5x − y = −49 →
  33. 33.x + 9y = 36 and 9x + y = 84 →
  34. 34.7x + y = −2 and x + 7y = 34 →
  35. 35.x − y = −6 and 2x + y = 9 →
  36. 36.4x + 9y = 5 and 9x + 4y = −5 →
  37. 37.x + 6y = 6 and x − 4y = −14 →
  38. 38.6x + 2y = −16 and 6x + 3y = −12 →
  39. 39.2x + 6y = −32 and 4x − y = 40 →
  40. 40.3x − 3y = −15 and 5x + 6y = 74 →

Answer key

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

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