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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 463 · 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 + 2y = 6 and 2x − 6y = −2 →
  2. 2.5x + 3y = 30 and 3x + 5y = 34 →
  3. 3.6x + 6y = 72 and x − 6y = −30 →
  4. 4.x − 5y = −23 and 6x + 6y = −30 →
  5. 5.3x + 6y = −21 and 2x − 2y = 22 →
  6. 6.2x − 4y = −14 and 5x + 4y = 21 →
  7. 7.6x + 3y = 21 and 2x + 6y = 22 →
  8. 8.5x + 2y = 23 and 6x − 3y = 60 →
  9. 9.2x + 3y = −9 and 4x − y = 31 →
  10. 10.4x − 2y = 48 and 2x − 6y = 54 →
  11. 11.3x + 6y = 57 and 6x + 3y = 60 →
  12. 12.7x + 6y = 19 and 6x + 7y = 20 →
  13. 13.x + 5y = −9 and 5x + y = −21 →
  14. 14.2x + 2y = −4 and 6x + 3y = −30 →
  15. 15.4x − y = 41 and 2x − 6y = 48 →
  16. 16.x + 4y = 11 and 4x + y = 29 →
  17. 17.3x + 4y = 36 and x + 5y = 23 →
  18. 18.2x − y = 7 and 4x − y = 11 →
  19. 19.3x − y = 22 and 4x + 3y = 25 →
  20. 20.2x − y = 23 and 6x + 3y = 15 →
  21. 21.3x − 6y = −12 and 6x + 3y = 36 →
  22. 22.x + 4y = −1 and 4x + y = −19 →
  23. 23.x − 3y = 18 and 5x + 5y = −70 →
  24. 24.x + 4y = −3 and 4x + 6y = 8 →
  25. 25.6x − 6y = −48 and 2x + y = −10 →
  26. 26.x + 2y = 2 and x + 3y = 7 →
  27. 27.7x + 2y = −4 and 2x + 7y = −59 →
  28. 28.6x − y = 27 and 5x − 3y = 16 →
  29. 29.6x + y = 15 and 2x + 6y = 22 →
  30. 30.4x + 2y = 6 and 2x + 4y = −24 →
  31. 31.2x − 3y = −7 and 3x + 2y = 35 →
  32. 32.6x + 5y = 75 and 3x + 5y = 60 →
  33. 33.2x − y = 9 and 3x − 4y = 6 →
  34. 34.x + 2y = −5 and 4x + 2y = −14 →
  35. 35.2x − 2y = 10 and 4x − 3y = 21 →
  36. 36.4x + 8y = 12 and 8x + 4y = 60 →
  37. 37.x + 7y = 63 and 7x + y = 57 →
  38. 38.2x + 7y = 58 and 7x + 2y = 23 →
  39. 39.5x + 5y = 30 and 3x − 4y = −17 →
  40. 40.2x − 4y = 42 and 4x + 4y = 0 →

Answer key

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

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