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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 264 · 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 + 4y = 50 and 6x − 5y = −4 →
  2. 2.7x + 3y = −14 and 3x + 7y = −46 →
  3. 3.x + 6y = 1 and 6x + y = −29 →
  4. 4.2x − 5y = −1 and 2x + 3y = 23 →
  5. 5.2x − 3y = 2 and 4x + 5y = 48 →
  6. 6.2x + 4y = −8 and 5x + y = −11 →
  7. 7.x + 3y = 13 and 3x + 2y = 11 →
  8. 8.x − 6y = −31 and x + 2y = 1 →
  9. 9.9x + 4y = 25 and 4x + 9y = 40 →
  10. 10.2x + 4y = 20 and 5x − 2y = 14 →
  11. 11.4x + 2y = −44 and 2x + 4y = −46 →
  12. 12.x − 5y = −29 and 4x + 6y = 14 →
  13. 13.4x − 2y = −36 and 5x + 6y = −11 →
  14. 14.x − 3y = 16 and 5x − y = 24 →
  15. 15.9x + 8y = −47 and 8x + 9y = −55 →
  16. 16.3x + y = 16 and x − 6y = −39 →
  17. 17.5x − y = 6 and 3x + 4y = −1 →
  18. 18.2x − 3y = 16 and 2x + 4y = −12 →
  19. 19.5x + 8y = 23 and 8x + 5y = 29 →
  20. 20.6x + 3y = −12 and 2x − y = −12 →
  21. 21.5x + 6y = 63 and 5x + 5y = 55 →
  22. 22.x − 2y = −7 and 6x − y = 2 →
  23. 23.5x + 6y = −14 and 2x + 5y = −16 →
  24. 24.3x + 6y = 42 and 6x + 4y = 60 →
  25. 25.x + y = 10 and 3x − 5y = 14 →
  26. 26.4x + 6y = 28 and 5x + 3y = −1 →
  27. 27.8x + 7y = 103 and 7x + 8y = 107 →
  28. 28.3x + 6y = 54 and 6x + 3y = 63 →
  29. 29.4x + 2y = 10 and 4x + 5y = 13 →
  30. 30.x − 2y = 16 and 6x + 3y = 36 →
  31. 31.3x − 6y = −21 and 2x − 6y = −30 →
  32. 32.4x + 5y = 51 and 5x + 4y = 57 →
  33. 33.x + 5y = 18 and x + 6y = 23 →
  34. 34.8x + 9y = 68 and 9x + 8y = 68 →
  35. 35.x + 7y = 32 and 7x + y = 32 →
  36. 36.2x − 6y = −60 and 4x + 2y = −8 →
  37. 37.x + 2y = 19 and 2x + y = 23 →
  38. 38.6x + y = 49 and 2x + 2y = 18 →
  39. 39.3x − 2y = −1 and 4x + 3y = 10 →
  40. 40.6x + y = 28 and 6x − 3y = 12 →

Answer key

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

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