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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 378 · 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 + 4y = −4 and 2x + 5y = −11 →
  2. 2.2x + 3y = −1 and 3x + 2y = 11 →
  3. 3.5x − 4y = 7 and 4x − 2y = 8 →
  4. 4.5x + 2y = 35 and 3x + 2y = 25 →
  5. 5.2x + 4y = −14 and 4x + 2y = 8 →
  6. 6.8x + 9y = 95 and 9x + 8y = 92 →
  7. 7.x − 5y = 12 and 4x − 4y = 0 →
  8. 8.x − 4y = −13 and 6x + 6y = −18 →
  9. 9.x + 7y = 56 and 7x + y = 56 →
  10. 10.2x + 2y = 26 and 3x − y = 23 →
  11. 11.2x − 6y = −24 and 6x − 4y = −2 →
  12. 12.2x + 3y = 24 and x − 5y = −1 →
  13. 13.6x + 9y = −111 and 9x + 6y = −114 →
  14. 14.6x + 6y = 12 and 3x + 4y = 7 →
  15. 15.7x + 2y = −30 and 2x + 7y = 30 →
  16. 16.6x + y = 22 and 3x − 5y = −11 →
  17. 17.x − 2y = 0 and x + 2y = 4 →
  18. 18.4x − 6y = 22 and 5x + 4y = 39 →
  19. 19.3x + 6y = 21 and 4x + y = 21 →
  20. 20.2x + y = −3 and 5x + 5y = 10 →
  21. 21.x + y = 1 and 2x + y = −2 →
  22. 22.x + 4y = 40 and 6x + 2y = 42 →
  23. 23.6x + 2y = 24 and 2x + 6y = 24 →
  24. 24.x + 7y = 5 and 7x + y = −13 →
  25. 25.9x + 3y = 99 and 3x + 9y = 105 →
  26. 26.x + 7y = −46 and 7x + y = 14 →
  27. 27.x + 8y = 11 and 8x + y = 25 →
  28. 28.5x + 4y = 43 and 5x − 3y = −6 →
  29. 29.2x − y = −20 and 5x + y = −22 →
  30. 30.x − 6y = 44 and 4x + 4y = −48 →
  31. 31.2x + 4y = 44 and 6x + 2y = 42 →
  32. 32.4x − 4y = 0 and x − 4y = −27 →
  33. 33.8x + 2y = −38 and 2x + 8y = 58 →
  34. 34.x + 8y = 3 and 8x + y = −39 →
  35. 35.5x + 5y = −25 and 6x − 5y = −19 →
  36. 36.x + 5y = 20 and 3x − 6y = −3 →
  37. 37.4x + 2y = −10 and 3x + 3y = −9 →
  38. 38.5x − 4y = 64 and 5x + 3y = 22 →
  39. 39.3x + 6y = 54 and 6x + 3y = 36 →
  40. 40.4x + 3y = 41 and x + y = 12 →

Answer key

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

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