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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 169 · 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. 1.2x − 5y = −42 and 4x + 5y = 36 →
  2. 2.2x − 3y = 12 and 2x + 4y = −2 →
  3. 3.5x + 5y = −70 and 3x + y = −26 →
  4. 4.x + 4y = 10 and 5x + 5y = 35 →
  5. 5.3x + 5y = −55 and 4x + 5y = −60 →
  6. 6.5x + 9y = −21 and 9x + 5y = −49 →
  7. 7.4x − 2y = −22 and x + 4y = 35 →
  8. 8.4x − 6y = −18 and 4x + 2y = 54 →
  9. 9.x − y = −1 and 4x + 2y = 14 →
  10. 10.3x + 2y = 9 and 2x + 3y = 11 →
  11. 11.x + 8y = 64 and 8x + y = −55 →
  12. 12.2x − 2y = 10 and x + 6y = −23 →
  13. 13.5x + 5y = 15 and x + 6y = 33 →
  14. 14.9x + 6y = 0 and 6x + 9y = −45 →
  15. 15.7x + 5y = 82 and 5x + 7y = 86 →
  16. 16.x + 2y = 16 and 2x + y = 5 →
  17. 17.2x − 4y = 36 and 5x + 2y = 30 →
  18. 18.x + 5y = −40 and 6x + 4y = −58 →
  19. 19.6x − 6y = −54 and 6x − y = −34 →
  20. 20.2x − 5y = −47 and 5x + 5y = 5 →
  21. 21.6x + 4y = 50 and 2x − 3y = 8 →
  22. 22.4x + y = −45 and x + 4y = −45 →
  23. 23.3x + 3y = 3 and 2x + 4y = −14 →
  24. 24.5x + 3y = 54 and 2x + 6y = 36 →
  25. 25.7x + 5y = 0 and 5x + 7y = 24 →
  26. 26.7x + 5y = 76 and 5x + 7y = 68 →
  27. 27.5x + 5y = 15 and 6x − 5y = −81 →
  28. 28.5x − y = 23 and 5x + y = 37 →
  29. 29.x + 6y = 10 and 5x + 3y = −31 →
  30. 30.3x + 9y = 54 and 9x + 3y = 90 →
  31. 31.4x − 3y = 7 and 3x + y = 15 →
  32. 32.2x + 2y = −28 and 3x − y = −6 →
  33. 33.4x + y = 18 and x + 4y = −3 →
  34. 34.x − 4y = −26 and 4x + 6y = 50 →
  35. 35.4x + 3y = −30 and 3x + 4y = −19 →
  36. 36.5x − 3y = −22 and 3x + 2y = −36 →
  37. 37.2x + 6y = 30 and 2x + y = 15 →
  38. 38.x − 5y = 9 and 6x + 5y = 19 →
  39. 39.x + 5y = 23 and 5x + y = 19 →
  40. 40.x + 4y = 32 and 2x − 4y = −20 →

Answer key

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

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