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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 858 · 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. 1.5x + 7y = −20 and 7x + 5y = −4 →
  2. 2.5x + 3y = 26 and 2x + 6y = 44 →
  3. 3.9x + 3y = 45 and 3x + 9y = 87 →
  4. 4.2x + y = 7 and x + 2y = −10 →
  5. 5.x − y = 10 and 2x + y = −4 →
  6. 6.x + 4y = −33 and x + y = −12 →
  7. 7.5x + 7y = 54 and 7x + 5y = 42 →
  8. 8.x − y = 4 and 5x − 3y = 16 →
  9. 9.x + 3y = 8 and 2x + 3y = 7 →
  10. 10.3x + 3y = 48 and x − 2y = −11 →
  11. 11.x − 3y = 6 and x + 3y = 12 →
  12. 12.4x + 3y = −18 and 4x − 2y = −48 →
  13. 13.x + 2y = 9 and 4x − 4y = −12 →
  14. 14.6x + y = 9 and 4x − 3y = 17 →
  15. 15.5x + 2y = 56 and 6x − 3y = 24 →
  16. 16.4x + 4y = 4 and 2x − y = 23 →
  17. 17.2x + 4y = −4 and 4x + 6y = −4 →
  18. 18.3x + 2y = 25 and 2x − 4y = −10 →
  19. 19.3x − 2y = 4 and 5x + y = 11 →
  20. 20.4x + 8y = 28 and 8x + 4y = 32 →
  21. 21.4x − 6y = −4 and 2x + 5y = 46 →
  22. 22.4x + 2y = −32 and 2x + 4y = −22 →
  23. 23.3x + 3y = −21 and 3x + 6y = −18 →
  24. 24.2x − 4y = −40 and x + 5y = 36 →
  25. 25.2x − 5y = −13 and 4x + 6y = 54 →
  26. 26.2x + 3y = 21 and 3x + y = 28 →
  27. 27.6x + 5y = 59 and x + 2y = 11 →
  28. 28.6x + 2y = 28 and 2x + 6y = −12 →
  29. 29.4x + 2y = 46 and 2x + 4y = 38 →
  30. 30.x − 2y = −1 and 2x + 2y = 10 →
  31. 31.4x + 2y = −42 and 5x + y = −39 →
  32. 32.3x + 8y = 47 and 8x + 3y = −3 →
  33. 33.4x + 9y = −58 and 9x + 4y = −33 →
  34. 34.8x + 6y = 66 and 6x + 8y = 74 →
  35. 35.x + 2y = 14 and 5x + y = 43 →
  36. 36.2x + y = −4 and 4x + 3y = −14 →
  37. 37.5x + 7y = 11 and 7x + 5y = 25 →
  38. 38.9x + 4y = 83 and 4x + 9y = 73 →
  39. 39.5x + 7y = 84 and 7x + 5y = 84 →
  40. 40.6x + 6y = −66 and x + 4y = −35 →

Answer key

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

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