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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 9 · 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 = −24 and x − 6y = 15 →
  2. 2.6x + 9y = 51 and 9x + 6y = 69 →
  3. 3.2x + 3y = 33 and 3x + 2y = 32 →
  4. 4.x − 4y = −16 and 6x + y = −46 →
  5. 5.6x + 4y = −26 and 2x − 2y = −22 →
  6. 6.8x + 2y = 32 and 2x + 8y = 68 →
  7. 7.7x + y = 61 and x + 7y = 43 →
  8. 8.4x + y = 43 and 4x + 2y = 50 →
  9. 9.5x + y = −5 and x + 2y = 8 →
  10. 10.7x + y = 52 and x + 7y = −20 →
  11. 11.5x + 2y = −8 and 6x + 6y = −6 →
  12. 12.3x + 3y = −39 and x − 3y = 15 →
  13. 13.2x + 3y = 22 and 2x + y = 10 →
  14. 14.x + 4y = −24 and 6x + 3y = 3 →
  15. 15.x + 4y = 14 and 2x + 3y = 13 →
  16. 16.x + 5y = 42 and 5x + y = 18 →
  17. 17.2x + 4y = 24 and 4x + 6y = 42 →
  18. 18.4x + 3y = 18 and 6x + y = 20 →
  19. 19.4x + y = 10 and 5x + 5y = 5 →
  20. 20.x − 2y = −4 and 6x + 3y = −9 →
  21. 21.3x + 2y = −28 and 2x − y = −14 →
  22. 22.6x + 3y = 0 and 5x − y = −14 →
  23. 23.2x + 6y = −2 and x − 3y = −13 →
  24. 24.7x + 6y = 44 and 6x + 7y = 47 →
  25. 25.x + 5y = 17 and 5x + y = 13 →
  26. 26.2x + 2y = 16 and x + 6y = 18 →
  27. 27.5x + 6y = 58 and 6x + 5y = 63 →
  28. 28.x − 6y = −3 and 3x + 2y = −29 →
  29. 29.3x − y = 16 and 5x + 2y = 45 →
  30. 30.x + 4y = −20 and 4x + y = −35 →
  31. 31.2x + 7y = −33 and 7x + 2y = −48 →
  32. 32.6x + 4y = 52 and 4x + 6y = 58 →
  33. 33.7x + 3y = 55 and 3x + 7y = 35 →
  34. 34.4x − 4y = 32 and x + 2y = −7 →
  35. 35.6x + 5y = 11 and 4x + 5y = 9 →
  36. 36.x + 6y = −44 and x + 4y = −32 →
  37. 37.6x + 4y = 30 and 2x + y = 7 →
  38. 38.x + 5y = 17 and 2x + 4y = 22 →
  39. 39.4x + 2y = 0 and 2x + 2y = −2 →
  40. 40.4x − 4y = −4 and 6x + 2y = 10 →

Answer key

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

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