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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 600 · 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 + 3y = 20 and x − 2y = −5 →
  2. 2.x − 5y = −44 and 3x + y = 12 →
  3. 3.4x − 4y = 36 and 3x + 4y = −1 →
  4. 4.3x + y = 0 and 5x + y = 2 →
  5. 5.6x + 7y = 104 and 7x + 6y = 104 →
  6. 6.x + 5y = 11 and x + y = −1 →
  7. 7.2x − 3y = −16 and 5x − y = 12 →
  8. 8.3x + 4y = 43 and 4x + 6y = 62 →
  9. 9.x + 5y = 43 and 4x + 4y = 44 →
  10. 10.4x + 4y = 8 and 6x + 5y = 9 →
  11. 11.4x + 4y = 60 and 4x + 3y = 54 →
  12. 12.2x + 5y = −12 and 5x + 2y = 12 →
  13. 13.x + 9y = 55 and 9x + y = 15 →
  14. 14.x + 6y = −4 and x − 2y = 4 →
  15. 15.4x − 5y = −20 and 6x + 3y = 54 →
  16. 16.x − 2y = −11 and 3x + 2y = 23 →
  17. 17.5x + 9y = −37 and 9x + 5y = 23 →
  18. 18.5x − y = −41 and x − 3y = 3 →
  19. 19.6x + 2y = 16 and 6x + 5y = 31 →
  20. 20.3x + 7y = 41 and 7x + 3y = 69 →
  21. 21.4x − 5y = −27 and 5x + 4y = −3 →
  22. 22.6x − 6y = 66 and 4x − y = 17 →
  23. 23.5x + 2y = 50 and x + 4y = 28 →
  24. 24.6x + y = 11 and 2x + 5y = 27 →
  25. 25.5x + 2y = −39 and 4x + 3y = −41 →
  26. 26.3x + 9y = 51 and 9x + 3y = −39 →
  27. 27.3x + 4y = 28 and x + 4y = 20 →
  28. 28.2x − 6y = −26 and 6x + 2y = 42 →
  29. 29.6x + 4y = 54 and 3x + 4y = 45 →
  30. 30.x + 2y = −4 and 6x + 6y = −30 →
  31. 31.x + 4y = 38 and 4x + y = 32 →
  32. 32.3x + 5y = −5 and 5x + 3y = 13 →
  33. 33.5x − 2y = −24 and 6x + 5y = −88 →
  34. 34.2x − y = 17 and 4x + 5y = 41 →
  35. 35.2x + 4y = 22 and 4x + 2y = 26 →
  36. 36.4x − 2y = 18 and 3x − y = 17 →
  37. 37.9x + 8y = −33 and 8x + 9y = −35 →
  38. 38.x + 6y = 30 and 6x + 5y = −6 →
  39. 39.6x − y = −27 and x + 6y = 51 →
  40. 40.6x + 5y = 16 and 5x + 6y = 17 →

Answer key

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

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