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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 178 · 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 + y = 15 and x + 2y = 21 →
  2. 2.5x + 6y = −38 and x + y = −6 →
  3. 3.x − y = −12 and 4x + 2y = 0 →
  4. 4.3x + y = 18 and 3x + 2y = 21 →
  5. 5.2x + 6y = 38 and 6x + 2y = 50 →
  6. 6.2x + 2y = −2 and x + 2y = 5 →
  7. 7.5x + 3y = 33 and 2x − 3y = 9 →
  8. 8.x + 6y = 22 and 6x + y = 27 →
  9. 9.4x − 4y = −44 and 4x − y = −32 →
  10. 10.4x − 3y = 11 and 6x + 6y = 90 →
  11. 11.2x + 7y = 34 and 7x + 2y = −16 →
  12. 12.3x + 8y = 31 and 8x + 3y = −9 →
  13. 13.5x − 2y = −9 and 6x − 5y = 10 →
  14. 14.4x + 4y = −12 and 5x + 6y = −14 →
  15. 15.x − y = 9 and 4x + 3y = 29 →
  16. 16.3x + 2y = 7 and 2x + 3y = 18 →
  17. 17.2x + 5y = −31 and 5x + 2y = 17 →
  18. 18.5x + y = 49 and x + 5y = 53 →
  19. 19.4x − y = 40 and 4x + y = 32 →
  20. 20.x − 4y = −23 and 3x + y = −4 →
  21. 21.6x + 4y = −36 and 3x − 2y = −30 →
  22. 22.6x + 2y = −42 and 2x + 6y = −62 →
  23. 23.2x − 5y = −28 and x − 4y = −20 →
  24. 24.9x + 7y = 112 and 7x + 9y = 112 →
  25. 25.4x + 7y = −44 and 7x + 4y = −11 →
  26. 26.5x − 2y = 17 and 6x − 2y = 18 →
  27. 27.7x + 6y = 103 and 6x + 7y = 105 →
  28. 28.8x + 6y = 10 and 6x + 8y = −10 →
  29. 29.6x + 3y = 45 and 3x + y = 18 →
  30. 30.x − 5y = −39 and 5x + 5y = 75 →
  31. 31.7x + 2y = 32 and 2x + 7y = −23 →
  32. 32.6x + 8y = 94 and 8x + 6y = 88 →
  33. 33.3x + y = −20 and 4x + 6y = −64 →
  34. 34.2x + 2y = 30 and 2x − 3y = 0 →
  35. 35.3x + y = 29 and x + 3y = 23 →
  36. 36.7x + 8y = 119 and 8x + 7y = 121 →
  37. 37.x − 4y = −7 and 6x − y = 4 →
  38. 38.2x + y = −2 and 5x + 4y = 7 →
  39. 39.x + y = −9 and x − 5y = −3 →
  40. 40.5x + 2y = −7 and 4x − 2y = −2 →

Answer key

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

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