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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 509 · 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. 1.2x + 3y = −18 and 6x + 2y = 2 →
  2. 2.5x + 2y = 22 and 4x − 4y = 68 →
  3. 3.2x + 3y = −5 and 2x + 6y = −2 →
  4. 4.6x − 2y = 4 and 4x + 3y = −19 →
  5. 5.3x + 3y = 30 and 2x + 3y = 21 →
  6. 6.3x + 2y = −4 and 3x + 4y = 4 →
  7. 7.2x + 4y = 10 and 5x + 4y = 19 →
  8. 8.2x − 5y = −45 and 2x − 3y = −31 →
  9. 9.2x + y = 1 and x + 2y = 14 →
  10. 10.x + 5y = 39 and 3x + 4y = 29 →
  11. 11.x + 6y = 40 and 3x − 3y = −48 →
  12. 12.x + 5y = 14 and 5x + y = −2 →
  13. 13.x + 3y = −1 and 3x + y = 13 →
  14. 14.6x + 2y = 40 and 5x − 6y = −5 →
  15. 15.3x + 2y = −21 and 3x − 4y = 33 →
  16. 16.9x + 7y = 29 and 7x + 9y = 19 →
  17. 17.5x − y = 36 and x + 2y = −6 →
  18. 18.4x + 4y = 8 and 6x + y = −13 →
  19. 19.5x − 2y = 53 and 6x − 6y = 78 →
  20. 20.4x + 5y = −19 and 5x + 4y = −17 →
  21. 21.3x − y = 17 and 2x − 3y = 9 →
  22. 22.3x − y = 24 and x + 6y = 27 →
  23. 23.x + 5y = 25 and 5x + 3y = −7 →
  24. 24.x − y = 1 and 3x − 5y = −7 →
  25. 25.5x + 3y = −2 and 4x + 5y = 1 →
  26. 26.4x + 6y = 14 and 6x + 4y = 36 →
  27. 27.4x + 2y = 16 and 4x − y = −2 →
  28. 28.x + 2y = −19 and 2x + y = −14 →
  29. 29.4x + 5y = 11 and 3x + y = 0 →
  30. 30.6x + y = 15 and x + 6y = 20 →
  31. 31.x − 6y = −56 and 2x + 3y = 23 →
  32. 32.2x + y = −17 and x + 2y = −10 →
  33. 33.x − 2y = −1 and 2x − 5y = −1 →
  34. 34.3x + 5y = −2 and 4x + 4y = 0 →
  35. 35.5x + 3y = 54 and x + 5y = 46 →
  36. 36.x + 7y = 20 and 7x + y = 44 →
  37. 37.6x + 3y = 57 and 3x + 6y = 51 →
  38. 38.7x + 3y = 17 and 3x + 7y = −27 →
  39. 39.3x − y = −7 and 2x − 4y = −8 →
  40. 40.2x + 3y = 4 and 3x + 2y = −9 →

Answer key

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

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