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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 73 · 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 = 44 and 2x + 5y = 48 →
  2. 2.5x + 4y = 44 and 4x + 5y = 37 →
  3. 3.4x + y = 13 and 4x + 3y = 23 →
  4. 4.4x + 2y = 2 and 3x + 4y = −11 →
  5. 5.3x − 2y = −10 and x − 6y = −14 →
  6. 6.3x − 6y = −39 and x − 4y = −21 →
  7. 7.3x + 8y = 34 and 8x + 3y = 54 →
  8. 8.6x + 7y = 99 and 7x + 6y = 96 →
  9. 9.7x + 9y = −32 and 9x + 7y = 0 →
  10. 10.9x + 3y = −15 and 3x + 9y = 3 →
  11. 11.x + 3y = 6 and 3x + y = −14 →
  12. 12.x + 4y = 5 and 3x − y = 28 →
  13. 13.6x − 2y = 18 and 4x − 4y = −12 →
  14. 14.2x + 6y = −64 and 2x + 3y = −37 →
  15. 15.7x + 6y = 117 and 6x + 7y = 117 →
  16. 16.x + 4y = 17 and 2x + 3y = 24 →
  17. 17.4x + 7y = 22 and 7x + 4y = 55 →
  18. 18.2x + 7y = 10 and 7x + 2y = −55 →
  19. 19.8x + 2y = 24 and 2x + 8y = 36 →
  20. 20.x + 2y = 23 and 3x + 4y = 55 →
  21. 21.4x + 5y = 9 and 3x + 2y = −9 →
  22. 22.x + 4y = −27 and 2x + 3y = −24 →
  23. 23.6x + 5y = 46 and 5x + 6y = 42 →
  24. 24.3x + 4y = 37 and 3x − 6y = −33 →
  25. 25.3x + 5y = 49 and 3x + 3y = 33 →
  26. 26.2x − 2y = −6 and x + 6y = −10 →
  27. 27.6x − 3y = −27 and x + y = −3 →
  28. 28.5x + 8y = 47 and 8x + 5y = 44 →
  29. 29.9x + 6y = −57 and 6x + 9y = −63 →
  30. 30.x − 6y = −5 and 3x + 6y = 9 →
  31. 31.2x − 3y = −14 and 5x − 3y = 1 →
  32. 32.3x + 8y = 65 and 8x + 3y = 45 →
  33. 33.x + y = −4 and 2x − 3y = −13 →
  34. 34.x + y = 13 and 6x + 3y = 60 →
  35. 35.9x + 6y = 15 and 6x + 9y = 45 →
  36. 36.4x + y = 23 and x + y = 8 →
  37. 37.2x + 6y = 10 and 6x + 2y = 14 →
  38. 38.3x + 3y = 9 and x + 6y = 13 →
  39. 39.3x + 2y = 37 and 5x − 4y = 3 →
  40. 40.x + 8y = 6 and 8x + y = −15 →

Answer key

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

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