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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 368 · 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 + 5y = −55 and 2x − 5y = −8 →
  2. 2.2x + y = −13 and 4x + 4y = −44 →
  3. 3.3x + 5y = 48 and 2x + 3y = 29 →
  4. 4.6x + y = 48 and 3x − 4y = 51 →
  5. 5.5x − 4y = −10 and 4x + 4y = 28 →
  6. 6.x + 8y = 45 and 8x + y = 45 →
  7. 7.3x − 2y = −13 and 4x + 4y = −4 →
  8. 8.8x + 2y = −14 and 2x + 8y = 4 →
  9. 9.5x + 5y = 55 and 6x − 6y = 30 →
  10. 10.x + 3y = 11 and 6x + y = 49 →
  11. 11.3x − 6y = −33 and 3x + 2y = 15 →
  12. 12.5x + 2y = −3 and 3x + 6y = −45 →
  13. 13.3x − 4y = −19 and 3x − y = −7 →
  14. 14.3x + 6y = 24 and 3x + 4y = 20 →
  15. 15.3x + 3y = 27 and 3x + 2y = 25 →
  16. 16.4x + 5y = 63 and 5x + 6y = 77 →
  17. 17.x − 6y = 51 and 4x + 5y = 1 →
  18. 18.4x + 3y = −7 and 3x − 5y = −27 →
  19. 19.5x + 8y = 42 and 8x + 5y = 36 →
  20. 20.6x + 3y = −3 and 3x − 2y = −33 →
  21. 21.6x + 2y = 46 and 6x − 2y = 14 →
  22. 22.2x − y = −9 and 2x − 6y = 6 →
  23. 23.7x + 5y = 6 and 5x + 7y = 18 →
  24. 24.x + 3y = 19 and 5x − y = −1 →
  25. 25.4x + 2y = 2 and 3x − 4y = 18 →
  26. 26.7x + 6y = −8 and 6x + 7y = 8 →
  27. 27.2x + 9y = 95 and 9x + 2y = 81 →
  28. 28.9x + 8y = −80 and 8x + 9y = −73 →
  29. 29.4x − 2y = −28 and x + 3y = −21 →
  30. 30.2x − 4y = 20 and x + 5y = −11 →
  31. 31.9x + 7y = 90 and 7x + 9y = 102 →
  32. 32.x + 3y = 28 and 2x + 4y = 40 →
  33. 33.7x + 5y = −78 and 5x + 7y = −66 →
  34. 34.3x + 7y = −46 and 7x + 3y = −54 →
  35. 35.2x + 5y = 53 and 6x − 6y = −30 →
  36. 36.4x − 3y = −39 and x + 2y = −7 →
  37. 37.6x + 3y = 45 and 3x + 6y = 18 →
  38. 38.2x − 5y = −29 and 6x − 4y = −10 →
  39. 39.5x + 4y = 45 and 3x + 3y = 30 →
  40. 40.x − 2y = −19 and x + 4y = 23 →

Answer key

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

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