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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 376 · 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. 1.3x − 4y = −3 and 2x + 5y = 44 →
  2. 2.x + 6y = −10 and x + y = 0 →
  3. 3.x + 2y = 3 and 6x + 6y = 6 →
  4. 4.7x + 5y = −8 and 5x + 7y = 8 →
  5. 5.6x − 2y = −32 and 5x + y = −16 →
  6. 6.5x + 9y = 80 and 9x + 5y = 88 →
  7. 7.4x − 6y = 56 and 5x + 3y = 7 →
  8. 8.4x + 3y = 19 and 3x + 4y = 9 →
  9. 9.3x + y = 15 and 3x − 6y = −27 →
  10. 10.4x + 5y = −10 and 5x + 4y = −17 →
  11. 11.2x + 5y = −9 and 4x + 2y = 6 →
  12. 12.4x + y = −12 and x + 4y = 12 →
  13. 13.x + 4y = −19 and 4x + y = 14 →
  14. 14.2x + y = 13 and 4x + 6y = 22 →
  15. 15.x + 4y = 26 and 5x + 6y = 46 →
  16. 16.3x − 6y = 30 and 2x + 6y = 10 →
  17. 17.6x + 2y = −8 and 3x + 5y = 28 →
  18. 18.3x + 5y = −17 and x + 2y = −6 →
  19. 19.5x + 9y = 28 and 9x + 5y = 28 →
  20. 20.3x − 2y = 29 and 2x + 2y = −4 →
  21. 21.7x + 2y = 16 and 2x + 7y = 11 →
  22. 22.6x + 2y = 64 and 2x + 3y = 40 →
  23. 23.4x + 6y = 64 and 6x − y = 16 →
  24. 24.x + 6y = 44 and 6x + y = −16 →
  25. 25.2x + 5y = −11 and 4x − 4y = 20 →
  26. 26.2x − 3y = 28 and 3x + 3y = −18 →
  27. 27.x − 2y = 1 and x − 3y = 0 →
  28. 28.8x + 2y = 72 and 2x + 8y = 48 →
  29. 29.6x + 5y = −3 and 5x + 6y = −19 →
  30. 30.6x + y = −15 and 6x − 5y = −33 →
  31. 31.6x + 6y = 78 and 5x − 3y = 1 →
  32. 32.8x + 7y = 77 and 7x + 8y = 73 →
  33. 33.4x + 5y = −32 and 6x − y = 20 →
  34. 34.3x + y = 8 and 2x + 6y = 16 →
  35. 35.5x + 2y = 8 and 3x − 2y = 8 →
  36. 36.x + y = 13 and 4x + 5y = 58 →
  37. 37.8x + 4y = −40 and 4x + 8y = 28 →
  38. 38.5x − y = 45 and 6x + y = 43 →
  39. 39.x + 2y = −11 and 6x + y = 0 →
  40. 40.2x + 2y = 6 and 5x − 6y = 26 →

Answer key

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

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