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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 936 · 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 + 3y = 41 and 3x + 5y = 47 →
  2. 2.4x − 2y = 16 and 2x + y = −4 →
  3. 3.6x + 8y = 2 and 8x + 6y = −30 →
  4. 4.3x + y = −15 and 4x + y = −18 →
  5. 5.9x + y = −69 and x + 9y = −61 →
  6. 6.x + 2y = −8 and 6x + 4y = 8 →
  7. 7.6x + 4y = 70 and x + 5y = 29 →
  8. 8.3x + 5y = 63 and 3x − 3y = −9 →
  9. 9.2x + 5y = −18 and 4x + y = −18 →
  10. 10.x − y = −4 and 2x + 3y = 27 →
  11. 11.4x + 3y = 18 and 6x + 5y = 26 →
  12. 12.4x + y = 14 and x + 4y = 11 →
  13. 13.4x + 3y = −40 and 3x + 4y = −44 →
  14. 14.4x + 5y = 21 and 4x − y = −33 →
  15. 15.8x + 4y = 88 and 4x + 8y = 80 →
  16. 16.6x + 8y = 76 and 8x + 6y = 64 →
  17. 17.6x − 6y = −24 and x + y = −12 →
  18. 18.7x + 3y = 8 and 3x + 7y = 32 →
  19. 19.6x + y = −45 and 3x + 6y = −6 →
  20. 20.9x + 7y = 53 and 7x + 9y = 27 →
  21. 21.x + 4y = −33 and 4x + y = −27 →
  22. 22.7x + 2y = −5 and 2x + 7y = 5 →
  23. 23.2x + 4y = −16 and 4x + 4y = −4 →
  24. 24.2x + 6y = 20 and 6x − 6y = −12 →
  25. 25.3x + 5y = 41 and 2x − 4y = −2 →
  26. 26.x + 3y = −20 and 3x + y = 12 →
  27. 27.9x + 4y = −7 and 4x + 9y = 33 →
  28. 28.5x + 8y = 4 and 8x + 5y = −17 →
  29. 29.x + y = 1 and 6x + 5y = 12 →
  30. 30.3x + 5y = −1 and 5x + 3y = −23 →
  31. 31.x − y = −12 and 6x + 6y = 24 →
  32. 32.3x + 2y = −37 and 4x + 3y = −52 →
  33. 33.x + 2y = 3 and 2x + y = 3 →
  34. 34.3x + 4y = −20 and 4x + 3y = −22 →
  35. 35.2x + 3y = 27 and 2x + y = 17 →
  36. 36.6x + 3y = −36 and 3x + 6y = −54 →
  37. 37.9x + 2y = −50 and 2x + 9y = 6 →
  38. 38.4x + y = 15 and 3x + 2y = 10 →
  39. 39.2x + 6y = −2 and 3x + 2y = 18 →
  40. 40.5x + 6y = −70 and x + 5y = −33 →

Answer key

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

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