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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 246 · 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 = 2 and 3x + 2y = −14 →
  2. 2.2x + 7y = 40 and 7x + 2y = 50 →
  3. 3.4x + y = 1 and 6x + 5y = 19 →
  4. 4.2x + y = 3 and x + 2y = −6 →
  5. 5.2x + 5y = −8 and 2x − 5y = 12 →
  6. 6.2x − 5y = 19 and 4x + 5y = −67 →
  7. 7.5x + 6y = 31 and x + 6y = 11 →
  8. 8.7x + 4y = 35 and 4x + 7y = 53 →
  9. 9.x − 4y = −27 and 4x + 6y = 68 →
  10. 10.4x + y = 25 and x + 4y = 25 →
  11. 11.6x + 5y = −17 and 5x + 4y = −15 →
  12. 12.2x − y = 2 and x + 2y = −14 →
  13. 13.6x + 2y = −10 and 2x + 5y = 1 →
  14. 14.9x + y = 49 and x + 9y = −39 →
  15. 15.4x + 6y = −48 and 3x + 3y = −27 →
  16. 16.2x + 9y = 27 and 9x + 2y = 83 →
  17. 17.4x + 8y = 72 and 8x + 4y = 84 →
  18. 18.6x − 6y = 6 and 2x + 5y = 23 →
  19. 19.x + 6y = −50 and 3x + 5y = −46 →
  20. 20.3x + 6y = 54 and 6x + 3y = 36 →
  21. 21.7x + 8y = 30 and 8x + 7y = 15 →
  22. 22.3x + 5y = 1 and 6x + 3y = −12 →
  23. 23.7x + 4y = −20 and 4x + 7y = −2 →
  24. 24.2x + 6y = −8 and 2x − 5y = 25 →
  25. 25.6x + y = 51 and x − 3y = −20 →
  26. 26.2x − 4y = 28 and x + 3y = −26 →
  27. 27.2x + 3y = 21 and 6x + 5y = 43 →
  28. 28.2x + y = 12 and 6x + 4y = 42 →
  29. 29.6x + 7y = 14 and 7x + 6y = −1 →
  30. 30.9x + 2y = 72 and 2x + 9y = 93 →
  31. 31.3x + 4y = 2 and 2x − 2y = −8 →
  32. 32.x + 4y = 19 and 4x + y = 16 →
  33. 33.2x + 4y = 44 and 3x − 5y = −11 →
  34. 34.2x + y = −12 and x + 2y = −12 →
  35. 35.5x + 3y = 3 and 3x + 5y = −11 →
  36. 36.5x + 3y = 46 and 2x − 5y = −25 →
  37. 37.4x − 5y = 1 and 3x + 5y = −8 →
  38. 38.3x + 6y = 9 and x + 5y = −6 →
  39. 39.2x − y = −10 and 5x − 6y = −18 →
  40. 40.5x + 6y = 63 and 6x + 3y = 42 →

Answer key

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

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