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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 850 · 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. 1.6x + 8y = 44 and 8x + 6y = 40 →
  2. 2.2x + 9y = −16 and 9x + 2y = 5 →
  3. 3.2x + 5y = −42 and 4x + y = −12 →
  4. 4.4x − 2y = 34 and 3x + y = 28 →
  5. 5.2x + 3y = 19 and 3x − 2y = 22 →
  6. 6.3x + 5y = 11 and 3x + 2y = 17 →
  7. 7.2x + 5y = 39 and 5x + 2y = 45 →
  8. 8.5x + 2y = 26 and 2x + 5y = 23 →
  9. 9.x + 4y = 3 and 4x + y = −33 →
  10. 10.x + 4y = 10 and 5x + 5y = 20 →
  11. 11.x + 6y = −51 and 3x − 5y = 8 →
  12. 12.2x + 4y = 30 and 4x + 2y = 24 →
  13. 13.2x + 9y = 6 and 9x + 2y = −50 →
  14. 14.9x + 3y = 72 and 3x + 9y = 0 →
  15. 15.6x − 3y = −15 and 3x − 5y = −32 →
  16. 16.2x + 3y = 0 and 3x + 2y = 15 →
  17. 17.5x − 2y = 36 and 6x + 4y = 56 →
  18. 18.8x + 3y = 32 and 3x + 8y = 67 →
  19. 19.5x + 3y = 36 and 4x + 3y = 30 →
  20. 20.5x − 6y = 3 and 6x + 6y = 96 →
  21. 21.4x + 2y = 50 and x + 3y = 35 →
  22. 22.8x + 5y = −18 and 5x + 8y = 18 →
  23. 23.4x + 5y = 33 and 2x + 2y = 16 →
  24. 24.5x − 5y = 20 and 3x + 6y = 3 →
  25. 25.3x + 9y = −60 and 9x + 3y = 12 →
  26. 26.4x − 2y = 6 and 6x + 3y = −45 →
  27. 27.3x + 2y = 0 and 2x − 5y = −57 →
  28. 28.4x − 5y = −37 and 5x + 2y = 28 →
  29. 29.2x + 8y = 50 and 8x + 2y = −10 →
  30. 30.8x + y = −28 and x + 8y = 28 →
  31. 31.4x − 5y = 33 and 4x − 2y = 30 →
  32. 32.x + 5y = 18 and 6x + 3y = 0 →
  33. 33.2x + 5y = 21 and 2x + y = 1 →
  34. 34.x − y = 3 and x + y = −15 →
  35. 35.5x + 5y = 50 and x + 6y = 40 →
  36. 36.3x + 4y = 10 and x + 2y = 6 →
  37. 37.x + y = −6 and 5x + 4y = −28 →
  38. 38.x − 3y = −17 and 4x − 5y = −40 →
  39. 39.3x + 2y = 41 and 6x + 6y = 96 →
  40. 40.6x + 4y = −42 and 6x + y = −51 →

Answer key

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

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