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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 181 · 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 + 3y = 1 and 3x + 2y = −1 →
  2. 2.5x + 6y = 78 and 3x − 2y = 2 →
  3. 3.x + y = 7 and 4x − 2y = 4 →
  4. 4.5x + 4y = −36 and 4x + 5y = −36 →
  5. 5.3x + 2y = 31 and 5x + 6y = 73 →
  6. 6.4x − 4y = 56 and 3x + 2y = 7 →
  7. 7.9x + 3y = −12 and 3x + 9y = 60 →
  8. 8.x − 3y = 20 and 6x + 3y = 15 →
  9. 9.5x + 5y = 5 and 2x + y = 3 →
  10. 10.4x + 5y = 27 and 4x + 6y = 26 →
  11. 11.6x + y = −10 and x + 6y = 10 →
  12. 12.4x − 4y = 48 and 5x + 2y = −3 →
  13. 13.2x + 2y = 10 and 4x + 3y = 16 →
  14. 14.3x + 7y = 17 and 7x + 3y = 13 →
  15. 15.3x + 2y = −28 and 2x + 6y = −42 →
  16. 16.4x + 3y = −3 and 3x + 4y = −18 →
  17. 17.2x + 6y = 68 and 4x + 4y = 64 →
  18. 18.x + 4y = 7 and 4x + y = 13 →
  19. 19.6x + 3y = 36 and 3x + 6y = −9 →
  20. 20.5x + 3y = 8 and x − 5y = 52 →
  21. 21.6x + 2y = −20 and 3x − 3y = −30 →
  22. 22.4x + y = −9 and 3x − y = −19 →
  23. 23.3x − y = 9 and 3x + 4y = −21 →
  24. 24.4x + 6y = 44 and 2x + y = 18 →
  25. 25.2x + y = 12 and 6x + 4y = 40 →
  26. 26.6x + 8y = 16 and 8x + 6y = 40 →
  27. 27.6x − 6y = 36 and 2x − 3y = 11 →
  28. 28.2x + 6y = 26 and 6x + 2y = 14 →
  29. 29.x + 4y = 9 and x + 6y = 11 →
  30. 30.5x + 4y = −29 and 3x + 5y = −33 →
  31. 31.6x + 3y = 24 and 3x + 4y = 22 →
  32. 32.x − 3y = −6 and 6x − y = −19 →
  33. 33.4x + 6y = −62 and x + 4y = −28 →
  34. 34.4x + y = 29 and x + 4y = −4 →
  35. 35.3x − y = 7 and x − 4y = −27 →
  36. 36.3x + 3y = −9 and 4x + 2y = −16 →
  37. 37.2x + 5y = 43 and 3x + 2y = 37 →
  38. 38.5x − 3y = 17 and 5x + 2y = −28 →
  39. 39.3x + 5y = −18 and 5x − 3y = 72 →
  40. 40.7x + y = −54 and x + 7y = 6 →

Answer key

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

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