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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 162 · 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.x − 4y = 20 and x + 5y = −7 →
  2. 2.6x + 5y = 29 and 5x + 6y = 15 →
  3. 3.3x + 8y = −17 and 8x + 3y = −27 →
  4. 4.5x + 6y = 3 and 6x + 5y = 19 →
  5. 5.3x − 4y = 44 and x + 2y = −2 →
  6. 6.2x + 4y = −14 and 2x − 2y = 4 →
  7. 7.4x − 2y = 14 and 4x − 5y = 5 →
  8. 8.x + 3y = 13 and 3x + y = −1 →
  9. 9.4x − 3y = 63 and x + y = 0 →
  10. 10.6x + y = −1 and 3x + 6y = −39 →
  11. 11.6x − y = 16 and x + y = −2 →
  12. 12.4x + 9y = 57 and 9x + 4y = −18 →
  13. 13.x − 5y = −40 and 3x + y = 24 →
  14. 14.6x + y = −37 and x + 6y = 23 →
  15. 15.x + 2y = 17 and 2x + y = 16 →
  16. 16.4x − 6y = 10 and 6x + y = 5 →
  17. 17.x + 2y = 12 and 5x + 4y = 18 →
  18. 18.2x + 6y = 46 and 3x + 3y = 39 →
  19. 19.4x + 3y = −19 and 3x − 5y = 22 →
  20. 20.5x + 9y = −17 and 9x + 5y = 3 →
  21. 21.x + y = −3 and 6x − 2y = −50 →
  22. 22.8x + 7y = 112 and 7x + 8y = 113 →
  23. 23.4x + 4y = −40 and x − y = 4 →
  24. 24.4x − 3y = 18 and x + 5y = 39 →
  25. 25.x − y = 6 and x + 5y = 12 →
  26. 26.3x + 4y = 47 and 4x + 3y = 51 →
  27. 27.5x + 4y = −25 and x − 6y = −39 →
  28. 28.3x + 7y = −54 and 7x + 3y = −6 →
  29. 29.3x + 6y = 69 and 6x + 3y = 57 →
  30. 30.5x + 2y = 34 and 2x + 5y = 22 →
  31. 31.x + 2y = −12 and 5x + 3y = −11 →
  32. 32.x + 2y = −8 and 3x − y = −17 →
  33. 33.5x + y = 13 and x + 5y = 41 →
  34. 34.4x + 3y = 28 and x + 2y = 17 →
  35. 35.x + 3y = −5 and 3x + y = 9 →
  36. 36.4x + 6y = −24 and 3x − 2y = −31 →
  37. 37.5x + y = 47 and x + 2y = 13 →
  38. 38.4x + 3y = 37 and 6x + 3y = 45 →
  39. 39.x + 4y = 1 and 3x − 3y = 18 →
  40. 40.4x + 6y = 10 and 5x + 2y = 18 →

Answer key

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

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