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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 464 · 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. 1.9x + 3y = −21 and 3x + 9y = 9 →
  2. 2.2x + 5y = 22 and 5x + 2y = 34 →
  3. 3.3x − y = 7 and 2x + 3y = 12 →
  4. 4.6x + y = 25 and x + 6y = 10 →
  5. 5.x + 7y = −17 and 7x + y = 25 →
  6. 6.2x + 5y = 35 and 3x + 6y = 39 →
  7. 7.x + 6y = −45 and 4x + 5y = −9 →
  8. 8.4x + y = −30 and 5x − 4y = −6 →
  9. 9.4x + 2y = 8 and 2x + 6y = −36 →
  10. 10.3x − 2y = 33 and 6x + y = 51 →
  11. 11.2x − 3y = 16 and 2x + 2y = 6 →
  12. 12.2x + 6y = 32 and 6x + 2y = 48 →
  13. 13.5x + y = −32 and x + 5y = −16 →
  14. 14.2x + 6y = 16 and 2x − 6y = −8 →
  15. 15.x − y = 14 and x + 4y = −31 →
  16. 16.4x + y = 14 and 6x − 5y = 8 →
  17. 17.5x + 7y = 47 and 7x + 5y = 37 →
  18. 18.x + 3y = 15 and 3x + y = 13 →
  19. 19.4x + 2y = −40 and 3x + 4y = −50 →
  20. 20.4x + 3y = 7 and 5x + 3y = 8 →
  21. 21.3x + 6y = 30 and 3x − 6y = 6 →
  22. 22.4x − 3y = 13 and 4x − 5y = 3 →
  23. 23.4x + 2y = 34 and 2x + 4y = 38 →
  24. 24.3x + 4y = −35 and 3x + 2y = −31 →
  25. 25.4x + 5y = −22 and 2x + 4y = −20 →
  26. 26.5x − 2y = 51 and x + 2y = −9 →
  27. 27.8x + 7y = 23 and 7x + 8y = 7 →
  28. 28.6x + 3y = −9 and 2x − 6y = 60 →
  29. 29.6x + 5y = −13 and 5x + 6y = −20 →
  30. 30.3x + 5y = 47 and 3x − 3y = −9 →
  31. 31.x − 6y = −24 and 3x + y = 23 →
  32. 32.2x + 2y = −28 and 5x + 3y = −52 →
  33. 33.9x + 6y = 63 and 6x + 9y = 57 →
  34. 34.4x − 3y = 9 and 6x + 5y = 99 →
  35. 35.4x + 9y = −33 and 9x + 4y = −58 →
  36. 36.2x − 6y = −40 and 3x − y = 4 →
  37. 37.3x + 9y = 30 and 9x + 3y = 18 →
  38. 38.9x + 6y = 21 and 6x + 9y = 9 →
  39. 39.3x − y = 36 and 4x + 6y = −18 →
  40. 40.2x + y = 7 and 2x − y = 25 →

Answer key

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

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