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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 299 · 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 + 7y = −38 and 7x + 2y = 2 →
  2. 2.2x + y = 15 and 2x − y = 1 →
  3. 3.7x + 6y = 33 and 6x + 7y = 32 →
  4. 4.4x + y = 45 and 2x + 4y = 54 →
  5. 5.4x + y = 11 and 3x + y = 7 →
  6. 6.9x + 5y = 117 and 5x + 9y = 121 →
  7. 7.x − y = −5 and 3x − 6y = −39 →
  8. 8.2x + 6y = −6 and 4x − 5y = −29 →
  9. 9.x − y = 7 and 5x − 4y = 36 →
  10. 10.3x − 6y = −15 and 3x − y = −5 →
  11. 11.3x + 2y = 11 and 2x + 3y = 14 →
  12. 12.2x − 5y = −12 and 4x + 3y = 2 →
  13. 13.4x + 5y = −17 and 2x + 5y = −31 →
  14. 14.6x + 2y = 12 and 5x − 2y = −1 →
  15. 15.6x + 2y = 30 and 2x + 6y = 26 →
  16. 16.2x − 6y = 66 and x + 4y = −30 →
  17. 17.6x + 3y = 6 and 6x + y = 10 →
  18. 18.2x + 6y = 46 and x − 2y = −17 →
  19. 19.6x − 5y = 39 and 6x + 2y = 60 →
  20. 20.4x − 2y = 44 and 6x + 2y = 36 →
  21. 21.2x + 2y = 32 and 5x + 6y = 87 →
  22. 22.2x + 2y = 2 and 2x − 2y = −34 →
  23. 23.2x + 6y = −22 and 6x + 2y = −34 →
  24. 24.2x + 5y = 17 and 5x + 2y = 32 →
  25. 25.8x + 3y = 59 and 3x + 8y = 84 →
  26. 26.2x + y = −1 and x − 4y = 22 →
  27. 27.x + 5y = 6 and 5x − 5y = 0 →
  28. 28.4x + y = 20 and 5x + 4y = 3 →
  29. 29.3x + 4y = −47 and 2x − 5y = 30 →
  30. 30.9x + 7y = 67 and 7x + 9y = 77 →
  31. 31.3x − 5y = −19 and 6x + 4y = −52 →
  32. 32.4x + 5y = 38 and 5x + 4y = 43 →
  33. 33.4x + y = −28 and 2x + 3y = 6 →
  34. 34.2x − 2y = −12 and 5x − 6y = −33 →
  35. 35.5x + 3y = 33 and 3x − y = 3 →
  36. 36.4x − 6y = 42 and 5x + 6y = 39 →
  37. 37.5x + 3y = 27 and 3x + 5y = 29 →
  38. 38.x + 2y = −20 and 2x + 5y = −46 →
  39. 39.3x + 2y = 11 and 2x + 6y = 12 →
  40. 40.8x + 2y = 40 and 2x + 8y = 70 →

Answer key

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

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