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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 799 · 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 − y = 5 and 5x + y = 44 →
  2. 2.3x − 5y = 23 and 2x + 2y = 10 →
  3. 3.7x + 3y = −33 and 3x + 7y = −37 →
  4. 4.6x + 3y = −12 and 3x + 6y = 30 →
  5. 5.4x − 6y = 22 and 3x + y = 0 →
  6. 6.2x + y = −8 and x + 2y = −13 →
  7. 7.3x + 2y = 43 and 2x + 3y = 42 →
  8. 8.x + y = 5 and 3x − 3y = −3 →
  9. 9.2x + y = 5 and x + 2y = −5 →
  10. 10.5x + y = −41 and 2x + 3y = −6 →
  11. 11.3x + 3y = 0 and x + 3y = 14 →
  12. 12.8x + 6y = −76 and 6x + 8y = −78 →
  13. 13.x − 6y = 0 and 5x − 6y = 24 →
  14. 14.3x + 4y = 2 and 5x − 6y = 16 →
  15. 15.6x + y = −41 and 5x + 3y = −32 →
  16. 16.5x + 3y = 7 and 3x + 2y = 4 →
  17. 17.5x + 3y = 14 and 3x + 5y = −14 →
  18. 18.2x + 3y = 33 and 3x + 2y = 32 →
  19. 19.x + 3y = 16 and 3x + y = 16 →
  20. 20.4x + 8y = 80 and 8x + 4y = 76 →
  21. 21.2x − 2y = 2 and 6x − y = 11 →
  22. 22.4x − 2y = −42 and 2x − 6y = −46 →
  23. 23.9x + 3y = 30 and 3x + 9y = 18 →
  24. 24.3x − 2y = −10 and 4x − y = −10 →
  25. 25.2x + 6y = −6 and 2x − 6y = 18 →
  26. 26.8x + 3y = −1 and 3x + 8y = −21 →
  27. 27.3x + 8y = 50 and 8x + 3y = 60 →
  28. 28.4x + 3y = 15 and 6x − 2y = −36 →
  29. 29.x + 2y = 11 and 5x − 5y = 10 →
  30. 30.3x + 3y = 6 and 2x + 3y = 0 →
  31. 31.6x + 5y = 53 and 6x + 3y = 51 →
  32. 32.3x − 2y = −4 and 3x − 6y = −36 →
  33. 33.x + 5y = −5 and 6x − 4y = 38 →
  34. 34.3x + 4y = 32 and 6x + y = 50 →
  35. 35.6x + 5y = 73 and 5x + 6y = 70 →
  36. 36.5x + 5y = −15 and 2x + 6y = 10 →
  37. 37.2x + 2y = 6 and 6x + 4y = 30 →
  38. 38.2x + 5y = −17 and 6x + 3y = −39 →
  39. 39.2x + 5y = −31 and 5x + 2y = −4 →
  40. 40.5x + 5y = 55 and 3x − 4y = −23 →

Answer key

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

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