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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 247 · 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 + 2y = 14 and x − y = 8 →
  2. 2.x + 2y = −10 and 2x + y = −2 →
  3. 3.3x + 2y = −2 and 2x + 3y = 12 →
  4. 4.3x + 4y = 5 and x + 3y = 0 →
  5. 5.6x + y = 53 and 2x + 3y = 31 →
  6. 6.5x + 4y = −18 and 5x + 3y = −11 →
  7. 7.3x − 6y = −60 and 5x + 4y = −16 →
  8. 8.x + 5y = 37 and 5x + y = 17 →
  9. 9.2x + y = −11 and 2x + 3y = −9 →
  10. 10.4x − 2y = −16 and 4x − 5y = −4 →
  11. 11.6x + y = 28 and x + 2y = −10 →
  12. 12.2x − 2y = −28 and 6x − 3y = −66 →
  13. 13.3x + 4y = 38 and 2x + y = 12 →
  14. 14.4x + 3y = −9 and 5x − y = −35 →
  15. 15.5x + 3y = 53 and 3x + 5y = 51 →
  16. 16.4x − y = −30 and x − 6y = −19 →
  17. 17.5x + 9y = 112 and 9x + 5y = 112 →
  18. 18.5x + 6y = 57 and 6x + 5y = 53 →
  19. 19.6x + 4y = −22 and 2x − y = −12 →
  20. 20.7x + y = −33 and x + 7y = 57 →
  21. 21.6x + 4y = 70 and x − 2y = 1 →
  22. 22.6x + 3y = 15 and x + 4y = 6 →
  23. 23.9x + 5y = 107 and 5x + 9y = 103 →
  24. 24.6x − 3y = 21 and 3x + 6y = 18 →
  25. 25.2x − y = 13 and 2x + 4y = −22 →
  26. 26.x + y = 0 and 4x − 4y = −32 →
  27. 27.x + 3y = −29 and 3x − y = 3 →
  28. 28.2x + 3y = 25 and 3x + 2y = 30 →
  29. 29.6x + 6y = −36 and 5x + 3y = −16 →
  30. 30.x + y = −5 and 5x − y = −49 →
  31. 31.5x + y = −9 and x + 6y = −25 →
  32. 32.5x + 3y = 10 and 3x + 5y = 22 →
  33. 33.6x + y = −1 and 6x − 4y = −26 →
  34. 34.2x + 9y = 56 and 9x + 2y = 21 →
  35. 35.x + 6y = −21 and 6x + y = −56 →
  36. 36.3x + 4y = −23 and 5x + 2y = −15 →
  37. 37.3x − 2y = 28 and 5x + 6y = 28 →
  38. 38.x + 6y = −35 and 4x − 6y = 70 →
  39. 39.6x + 4y = 22 and x − y = 2 →
  40. 40.2x + 3y = 10 and x − 6y = −40 →

Answer key

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

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