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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 324 · 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 − 6y = 45 and x − 6y = 33 →
  2. 2.x + y = 7 and 3x − 5y = 5 →
  3. 3.3x + 6y = 18 and 6x + 3y = −27 →
  4. 4.8x + 9y = −75 and 9x + 8y = −78 →
  5. 5.2x + 6y = −34 and 6x + 2y = −38 →
  6. 6.6x − 4y = 50 and 2x + 5y = 23 →
  7. 7.8x + 7y = 52 and 7x + 8y = 53 →
  8. 8.x + 6y = 5 and x + 5y = 4 →
  9. 9.4x + 2y = −6 and x + y = 0 →
  10. 10.6x − 2y = −28 and 6x + y = −22 →
  11. 11.3x − 5y = −29 and x − 6y = −27 →
  12. 12.x + 3y = 0 and 3x + y = −24 →
  13. 13.6x − y = 14 and 6x + 4y = −26 →
  14. 14.8x + 9y = −23 and 9x + 8y = −28 →
  15. 15.8x + 2y = 62 and 2x + 8y = 68 →
  16. 16.3x + 4y = 5 and 4x + 3y = 9 →
  17. 17.5x + 5y = 85 and x + 5y = 49 →
  18. 18.x + 4y = 23 and 2x + 4y = 30 →
  19. 19.4x + 3y = 34 and 4x + y = 22 →
  20. 20.3x − y = −18 and 6x + 6y = −108 →
  21. 21.9x + 7y = 130 and 7x + 9y = 126 →
  22. 22.4x + 2y = −4 and 2x + 4y = −20 →
  23. 23.5x − 5y = −50 and 5x + 2y = −22 →
  24. 24.x + 5y = 11 and 5x + y = 31 →
  25. 25.5x + 3y = 2 and 3x + 5y = −18 →
  26. 26.6x + 3y = −42 and 6x + 4y = −46 →
  27. 27.2x + 9y = 43 and 9x + 2y = 1 →
  28. 28.3x + y = −15 and 4x + y = −21 →
  29. 29.5x + 3y = −11 and x − 6y = 11 →
  30. 30.4x + 3y = −12 and 3x + y = 1 →
  31. 31.6x + 4y = 64 and x + y = 12 →
  32. 32.3x − 5y = 23 and 3x + 4y = 14 →
  33. 33.3x + 5y = 28 and 5x + 3y = 20 →
  34. 34.5x + 3y = −58 and 3x + y = −30 →
  35. 35.4x + 3y = 30 and 4x + y = 18 →
  36. 36.5x + 4y = −2 and x + 6y = −42 →
  37. 37.4x + 5y = 25 and 6x + y = −21 →
  38. 38.2x + 8y = −28 and 8x + 2y = −52 →
  39. 39.8x + 6y = 102 and 6x + 8y = 94 →
  40. 40.2x + 4y = −2 and 4x + 2y = −22 →

Answer key

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

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