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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 581 · 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.x + 4y = −32 and 4x + y = −23 →
  2. 2.6x + 2y = −24 and 2x + 6y = 40 →
  3. 3.4x + 2y = 26 and 6x + 4y = 44 →
  4. 4.9x + 6y = 87 and 6x + 9y = 63 →
  5. 5.x + 9y = −5 and 9x + y = 35 →
  6. 6.2x − 3y = −12 and x + 2y = 15 →
  7. 7.2x + y = −12 and 5x + 5y = −25 →
  8. 8.8x + 6y = 80 and 6x + 8y = 74 →
  9. 9.3x − 6y = 60 and 6x − y = 32 →
  10. 10.3x − 4y = −55 and 3x − 2y = −41 →
  11. 11.2x + 3y = −5 and x + 6y = 2 →
  12. 12.9x + y = 47 and x + 9y = 23 →
  13. 13.2x + 3y = −12 and 4x − 6y = 48 →
  14. 14.4x + 7y = −56 and 7x + 4y = −65 →
  15. 15.4x + y = 13 and 5x + 5y = 20 →
  16. 16.x + 4y = 13 and 4x + y = 22 →
  17. 17.6x − 4y = 42 and 5x − 4y = 39 →
  18. 18.4x + 2y = −22 and 5x + 4y = −38 →
  19. 19.6x − 6y = −6 and 2x + y = 7 →
  20. 20.6x + 4y = 10 and 4x + 5y = −5 →
  21. 21.4x − 3y = 20 and 4x − 6y = 8 →
  22. 22.4x − 4y = 36 and x + 4y = −6 →
  23. 23.3x − 4y = 47 and x − y = 13 →
  24. 24.2x − y = −2 and 3x + 4y = 41 →
  25. 25.5x − y = 9 and 6x + y = 13 →
  26. 26.x + 7y = −34 and 7x + y = 50 →
  27. 27.4x + 8y = 80 and 8x + 4y = 64 →
  28. 28.x + 2y = −3 and 2x + 5y = −3 →
  29. 29.4x + 3y = −4 and x + y = 1 →
  30. 30.5x + 3y = 23 and x + 2y = 13 →
  31. 31.2x + y = −14 and 2x − 6y = 42 →
  32. 32.6x + 3y = 54 and 3x + 6y = 54 →
  33. 33.5x + 2y = 17 and 4x − 3y = 55 →
  34. 34.2x + 5y = 33 and 2x + 2y = 24 →
  35. 35.3x + 3y = 0 and 4x + y = −27 →
  36. 36.x + y = 2 and 4x + 6y = 16 →
  37. 37.4x + 6y = 56 and 5x + y = 44 →
  38. 38.x − 3y = 21 and 3x + 5y = −63 →
  39. 39.x − 2y = −3 and 3x + 6y = 63 →
  40. 40.5x + 3y = 6 and x + 4y = 25 →

Answer key

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

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