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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 290 · 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. 1.3x + 4y = 6 and 4x + y = 21 →
  2. 2.3x − 5y = 4 and 5x + y = 16 →
  3. 3.x + y = 0 and 3x + y = 8 →
  4. 4.5x + 2y = −36 and 4x + 5y = −39 →
  5. 5.4x + 4y = 24 and x + 6y = 16 →
  6. 6.4x + 4y = 32 and 3x + 2y = 23 →
  7. 7.2x + 5y = 8 and 5x + 2y = −1 →
  8. 8.5x − 2y = −36 and x + 2y = 0 →
  9. 9.2x + 6y = 24 and 6x + 2y = −40 →
  10. 10.9x + 7y = −11 and 7x + 9y = −5 →
  11. 11.5x − 6y = −29 and 4x + 3y = 47 →
  12. 12.x − 2y = −14 and 2x + y = 12 →
  13. 13.8x + 4y = 12 and 4x + 8y = −48 →
  14. 14.4x + 8y = 92 and 8x + 4y = 100 →
  15. 15.x + 6y = 45 and 2x + y = 13 →
  16. 16.4x + 2y = −36 and 2x + 4y = −24 →
  17. 17.9x + y = 26 and x + 9y = −6 →
  18. 18.5x − 3y = 39 and x + 5y = −37 →
  19. 19.4x + 9y = 40 and 9x + 4y = 25 →
  20. 20.6x + y = −35 and x + 6y = 0 →
  21. 21.3x − 2y = 19 and x + y = 8 →
  22. 22.3x + y = 12 and x + 3y = 12 →
  23. 23.2x + 5y = 12 and 5x + 2y = 9 →
  24. 24.6x + 6y = −48 and 3x − y = −20 →
  25. 25.3x + 7y = 48 and 7x + 3y = 72 →
  26. 26.x − y = −6 and 6x + 6y = 48 →
  27. 27.6x + 2y = −40 and 4x + 5y = −34 →
  28. 28.2x + 4y = 36 and 4x + 5y = 54 →
  29. 29.2x + 4y = 14 and 4x + 2y = 16 →
  30. 30.x + 4y = 41 and 4x + 5y = 65 →
  31. 31.4x + 2y = 24 and 2x + 4y = 30 →
  32. 32.2x + 5y = 29 and 5x + 2y = 20 →
  33. 33.6x + 3y = 0 and 6x + 5y = −16 →
  34. 34.9x + 4y = 63 and 4x + 9y = 93 →
  35. 35.5x + y = 39 and 5x + 4y = 51 →
  36. 36.4x + 4y = −8 and 2x − 6y = −28 →
  37. 37.3x + 7y = 10 and 7x + 3y = −30 →
  38. 38.2x − 2y = 30 and 5x + y = 33 →
  39. 39.2x − y = 1 and 4x + 4y = 20 →
  40. 40.5x + 7y = −32 and 7x + 5y = −16 →

Answer key

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

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