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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 343 · 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. 1.3x − 2y = 11 and 2x + y = 19 →
  2. 2.2x + 3y = 25 and 3x + 4y = 34 →
  3. 3.4x + 5y = 21 and x + 4y = 30 →
  4. 4.7x + 5y = 36 and 5x + 7y = 12 →
  5. 5.x + 4y = 15 and 5x − 6y = −55 →
  6. 6.2x + y = 5 and 3x + 6y = 3 →
  7. 7.3x + 7y = 2 and 7x + 3y = −22 →
  8. 8.7x + 4y = 63 and 4x + 7y = 69 →
  9. 9.2x + 3y = −22 and 5x − y = −4 →
  10. 10.5x − 5y = 35 and 2x + y = −1 →
  11. 11.2x − 2y = 8 and 3x + 4y = −2 →
  12. 12.x − 3y = 3 and 6x + 5y = 41 →
  13. 13.5x + y = 9 and 6x + 6y = 30 →
  14. 14.x + 4y = 13 and x + 5y = 16 →
  15. 15.5x + 3y = 69 and 6x + 2y = 70 →
  16. 16.9x + 7y = 100 and 7x + 9y = 92 →
  17. 17.2x − 2y = −4 and x − 6y = −42 →
  18. 18.5x + 2y = −17 and 2x + 5y = −32 →
  19. 19.x + 6y = −43 and 3x + 2y = −17 →
  20. 20.x + 6y = 21 and 5x + 3y = 51 →
  21. 21.9x + 8y = 81 and 8x + 9y = 89 →
  22. 22.5x − 2y = −41 and 4x + 5y = −13 →
  23. 23.3x + 6y = 15 and 4x + 4y = 4 →
  24. 24.5x + 7y = 59 and 7x + 5y = 49 →
  25. 25.x + 6y = 30 and x + 5y = 26 →
  26. 26.x − 5y = 49 and 2x + 4y = −14 →
  27. 27.3x + 9y = −66 and 9x + 3y = −30 →
  28. 28.5x − y = −45 and x + 2y = 2 →
  29. 29.8x + y = 37 and x + 8y = 44 →
  30. 30.3x + y = 27 and x + 2y = 24 →
  31. 31.x + 6y = −28 and 6x + y = 7 →
  32. 32.4x + y = 29 and 2x + 4y = −10 →
  33. 33.3x + 7y = 25 and 7x + 3y = 45 →
  34. 34.3x + 3y = −12 and 2x − 2y = −12 →
  35. 35.2x − 3y = 37 and 2x − y = 19 →
  36. 36.4x + y = 9 and x + 4y = −9 →
  37. 37.2x + 3y = 18 and 3x + 2y = 17 →
  38. 38.5x + 5y = 0 and 6x + 4y = −18 →
  39. 39.x + 4y = −22 and x + 2y = −10 →
  40. 40.4x + 3y = −33 and x − 6y = −15 →

Answer key

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

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