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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 473 · 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. 1.4x + y = 11 and 3x + 5y = 4 →
  2. 2.6x − 2y = 18 and 4x + y = 19 →
  3. 3.8x + 3y = −28 and 3x + 8y = −38 →
  4. 4.5x − 2y = 26 and 4x + 5y = 34 →
  5. 5.5x + 5y = 30 and x + 5y = 14 →
  6. 6.5x − 5y = 10 and 4x + 2y = 50 →
  7. 7.3x − 6y = 18 and x + 2y = 2 →
  8. 8.6x + 3y = −9 and 3x + 6y = 36 →
  9. 9.5x − 5y = 75 and x − 6y = 45 →
  10. 10.x + 4y = −23 and 2x + 5y = −34 →
  11. 11.2x + 9y = 35 and 9x + 2y = −35 →
  12. 12.6x + 6y = 24 and 6x − y = 10 →
  13. 13.2x + 5y = −37 and x − 3y = 9 →
  14. 14.2x − 3y = −17 and 5x + 4y = 15 →
  15. 15.4x + 5y = −42 and 5x + 4y = −39 →
  16. 16.x + 2y = −13 and 2x + y = −11 →
  17. 17.6x + 4y = 6 and 5x + y = −9 →
  18. 18.3x + 4y = 16 and 3x − 6y = −54 →
  19. 19.x + 2y = 1 and x + 4y = 7 →
  20. 20.2x + 3y = −15 and 6x − y = 45 →
  21. 21.5x − 4y = 34 and 2x + y = −2 →
  22. 22.3x + 3y = 3 and 5x − 2y = −44 →
  23. 23.2x + 8y = 24 and 8x + 2y = 66 →
  24. 24.6x + 7y = 46 and 7x + 6y = 45 →
  25. 25.4x + y = −1 and 6x + y = −5 →
  26. 26.x + 7y = 30 and 7x + y = 66 →
  27. 27.5x + 2y = 48 and 5x + 6y = 64 →
  28. 28.x − 2y = 11 and x + y = −1 →
  29. 29.5x + 6y = 14 and x − 2y = −10 →
  30. 30.5x − 3y = −8 and 5x − y = 4 →
  31. 31.6x + 5y = −9 and 4x − 3y = 51 →
  32. 32.5x + 6y = −59 and 3x + 5y = −48 →
  33. 33.4x + 5y = −4 and x − 2y = 12 →
  34. 34.6x − 6y = 30 and 5x + 4y = 52 →
  35. 35.3x − 4y = 21 and 4x + 3y = 3 →
  36. 36.x + 2y = −18 and 6x − 6y = −18 →
  37. 37.x + 2y = 13 and 2x + y = 20 →
  38. 38.5x + 6y = −1 and 6x − 2y = 54 →
  39. 39.3x + 2y = 0 and 2x − 4y = −48 →
  40. 40.7x + 9y = 70 and 9x + 7y = 58 →

Answer key

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

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