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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 201 · 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. 1.4x + 4y = −4 and x + 3y = −17 →
  2. 2.6x + 5y = −24 and 4x + y = −2 →
  3. 3.8x + 7y = 25 and 7x + 8y = 35 →
  4. 4.7x + y = −45 and x + 7y = 21 →
  5. 5.3x + 5y = 61 and x + 3y = 31 →
  6. 6.8x + 2y = 28 and 2x + 8y = 22 →
  7. 7.4x + 4y = 0 and 5x + 6y = −5 →
  8. 8.2x − 5y = −46 and 5x + 5y = 25 →
  9. 9.4x + 3y = −15 and 5x − y = −14 →
  10. 10.9x + 8y = −26 and 8x + 9y = −25 →
  11. 11.5x + 3y = −17 and 2x + 2y = −14 →
  12. 12.6x + 2y = 22 and 2x + 5y = 16 →
  13. 13.6x + 4y = 62 and 2x + 5y = 28 →
  14. 14.6x − y = 11 and 5x + 2y = 29 →
  15. 15.3x + 4y = 7 and x − 6y = 39 →
  16. 16.3x − 6y = 18 and 2x + 3y = −37 →
  17. 17.5x + 3y = 14 and 2x − 3y = 14 →
  18. 18.2x + y = 21 and x + 2y = 18 →
  19. 19.x − 2y = 6 and 3x + 3y = 9 →
  20. 20.4x − 5y = −41 and 5x + 5y = −40 →
  21. 21.2x − 6y = −22 and 5x + 6y = 71 →
  22. 22.2x + 5y = 30 and 2x + 6y = 38 →
  23. 23.3x − 6y = 24 and x + 5y = −6 →
  24. 24.4x + 6y = −26 and 3x + 3y = −15 →
  25. 25.x + 2y = 17 and 2x + y = 19 →
  26. 26.2x − 6y = 20 and 4x + y = −12 →
  27. 27.x + 3y = 10 and 5x + 6y = −4 →
  28. 28.2x + y = 10 and 4x − 4y = 56 →
  29. 29.6x − 4y = 34 and 5x + 5y = −5 →
  30. 30.5x − y = 33 and 5x + 5y = 15 →
  31. 31.x + y = 2 and 4x − 2y = 44 →
  32. 32.2x + y = 12 and x + 3y = 26 →
  33. 33.5x − 2y = −20 and 3x + 2y = 4 →
  34. 34.x − 6y = 12 and 3x + 3y = 15 →
  35. 35.x − 5y = −11 and 3x + 5y = 47 →
  36. 36.3x + y = −7 and 6x − y = −20 →
  37. 37.2x − 4y = −4 and 2x + 4y = 20 →
  38. 38.6x + 2y = 6 and 2x − y = 12 →
  39. 39.5x + 9y = 68 and 9x + 5y = 44 →
  40. 40.2x + 6y = 22 and 2x − 4y = 2 →

Answer key

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

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