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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 310 · 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 + 2y = 51 and 6x − 5y = 39 →
  2. 2.2x + y = −16 and 6x + y = −32 →
  3. 3.5x − 3y = 14 and 4x − 2y = 14 →
  4. 4.x + y = −3 and 4x + 3y = −13 →
  5. 5.2x − y = 21 and 2x + 2y = 0 →
  6. 6.6x + 8y = 62 and 8x + 6y = 50 →
  7. 7.6x + y = −29 and 3x + 6y = −9 →
  8. 8.4x − 3y = 11 and x − 2y = 14 →
  9. 9.3x + 2y = 15 and 4x + y = 25 →
  10. 10.3x + y = −23 and 2x + y = −17 →
  11. 11.x − 4y = 5 and x − 2y = 7 →
  12. 12.9x + 3y = 21 and 3x + 9y = −33 →
  13. 13.3x − 6y = 0 and 4x + 4y = 36 →
  14. 14.x + 6y = 19 and 5x − 3y = −4 →
  15. 15.2x + 4y = −18 and 2x − y = 17 →
  16. 16.4x + 2y = 24 and 3x + 4y = 28 →
  17. 17.5x + 3y = 14 and 6x + 4y = 14 →
  18. 18.6x + 8y = 16 and 8x + 6y = 40 →
  19. 19.8x + 2y = 8 and 2x + 8y = −58 →
  20. 20.5x + 4y = 42 and 4x + 5y = 48 →
  21. 21.2x + 4y = 46 and x + y = 16 →
  22. 22.3x + y = 5 and x + 3y = −1 →
  23. 23.3x + 4y = 46 and 4x + 3y = 45 →
  24. 24.5x + 3y = 49 and 6x + 2y = 46 →
  25. 25.4x − 2y = −42 and x + 5y = 17 →
  26. 26.x + 2y = 5 and 4x − 5y = 7 →
  27. 27.6x − 5y = −17 and 5x + 5y = −5 →
  28. 28.2x − 3y = 20 and 6x − y = 44 →
  29. 29.2x + 9y = 13 and 9x + 2y = 20 →
  30. 30.2x − 6y = 28 and 3x − 6y = 36 →
  31. 31.3x + 5y = 51 and 4x − 3y = −19 →
  32. 32.3x + 5y = −2 and 2x + 2y = −4 →
  33. 33.2x + 5y = 17 and 5x + 4y = 17 →
  34. 34.x + 4y = 21 and 6x + y = 57 →
  35. 35.x + 5y = −33 and 5x + y = 27 →
  36. 36.x − 3y = −18 and x + y = 18 →
  37. 37.6x + 5y = −42 and 4x − 3y = 10 →
  38. 38.2x + 5y = −5 and 2x + 2y = −8 →
  39. 39.9x + 7y = 2 and 7x + 9y = −2 →
  40. 40.x + 2y = 13 and 5x + 6y = 53 →

Answer key

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

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