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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 252 · 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 + 9y = 4 and 9x + y = −44 →
  2. 2.5x + 6y = 22 and 4x + 2y = −2 →
  3. 3.2x + 5y = 21 and 5x + 2y = −21 →
  4. 4.9x + y = 6 and x + 9y = −26 →
  5. 5.9x + y = −1 and x + 9y = 71 →
  6. 6.3x + y = 0 and 6x + 6y = −36 →
  7. 7.6x + y = 18 and x + 6y = 38 →
  8. 8.6x + 3y = 9 and 3x + 6y = −9 →
  9. 9.6x + 7y = −44 and 7x + 6y = −34 →
  10. 10.6x + 2y = −56 and 6x + 4y = −70 →
  11. 11.8x + 9y = −1 and 9x + 8y = −16 →
  12. 12.5x − 3y = 27 and 6x − 3y = 30 →
  13. 13.x + y = 7 and 4x + 3y = 23 →
  14. 14.3x + 9y = −36 and 9x + 3y = 12 →
  15. 15.8x + 4y = −72 and 4x + 8y = −48 →
  16. 16.8x + 3y = 53 and 3x + 8y = 13 →
  17. 17.4x + 6y = 60 and 5x + 6y = 63 →
  18. 18.2x + 2y = −4 and 5x + y = 18 →
  19. 19.2x − 2y = −26 and 3x + 2y = −14 →
  20. 20.3x + 2y = 32 and 4x + 5y = 59 →
  21. 21.3x + y = −27 and x − 4y = 4 →
  22. 22.4x + 2y = 22 and 6x + 6y = 24 →
  23. 23.3x + 6y = 33 and 6x + 3y = 30 →
  24. 24.5x + y = 40 and x + 5y = 32 →
  25. 25.5x + 6y = −11 and 5x − y = −39 →
  26. 26.x − 4y = −3 and x + y = 2 →
  27. 27.3x + 6y = 15 and 6x + 3y = −6 →
  28. 28.x + 2y = −1 and 2x + y = 13 →
  29. 29.x + 2y = 21 and x + 3y = 28 →
  30. 30.7x + 2y = 13 and 2x + 7y = −22 →
  31. 31.x + 4y = 33 and 6x + 2y = 44 →
  32. 32.4x − 6y = 12 and 2x + 4y = −36 →
  33. 33.4x + 3y = −9 and 3x + 3y = −12 →
  34. 34.5x − 3y = −3 and x − 6y = −33 →
  35. 35.5x − 5y = −75 and 5x − 3y = −63 →
  36. 36.2x + y = −7 and 6x − 2y = −46 →
  37. 37.4x + 2y = −10 and 4x + y = −15 →
  38. 38.x + 4y = 13 and 4x + y = 7 →
  39. 39.9x + y = 35 and x + 9y = −5 →
  40. 40.3x − y = 15 and x + 6y = 43 →

Answer key

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

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