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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 425 · 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 − y = −7 and 2x + 3y = −34 →
  2. 2.5x + 8y = 51 and 8x + 5y = 27 →
  3. 3.6x + 4y = −32 and 6x + 3y = −33 →
  4. 4.6x − 3y = −9 and 2x − 3y = −5 →
  5. 5.x + 9y = −21 and 9x + y = −29 →
  6. 6.2x + 3y = 19 and 3x + 2y = 21 →
  7. 7.7x + 5y = −20 and 5x + 7y = −4 →
  8. 8.5x + 7y = 69 and 7x + 5y = 63 →
  9. 9.3x + y = −7 and 2x + y = −2 →
  10. 10.2x − 6y = 16 and 4x + y = −20 →
  11. 11.3x + 3y = −18 and 3x − y = −26 →
  12. 12.5x − 3y = −28 and x − 5y = −32 →
  13. 13.4x + 9y = 66 and 9x + 4y = 51 →
  14. 14.2x + 4y = 14 and 6x + 6y = 24 →
  15. 15.3x − y = −13 and 2x + y = 3 →
  16. 16.6x + 7y = 64 and 7x + 6y = 66 →
  17. 17.3x + 3y = 0 and 2x − y = 3 →
  18. 18.8x + y = 58 and x + 8y = 23 →
  19. 19.3x + 3y = 9 and 2x + 3y = 7 →
  20. 20.x + 2y = 4 and 6x − y = 50 →
  21. 21.2x − 5y = −12 and x − 6y = −27 →
  22. 22.x + 6y = −36 and 4x − 4y = 52 →
  23. 23.6x − 3y = 15 and x − 5y = −38 →
  24. 24.4x + 5y = 52 and 5x + 4y = 47 →
  25. 25.9x + 7y = −52 and 7x + 9y = −44 →
  26. 26.5x + 3y = −22 and 4x + 2y = −14 →
  27. 27.6x − y = −13 and 4x − 3y = −25 →
  28. 28.6x + 3y = 48 and 6x + 5y = 56 →
  29. 29.8x + 6y = 36 and 6x + 8y = 34 →
  30. 30.7x + 6y = 49 and 6x + 7y = 55 →
  31. 31.3x + 4y = 51 and x + 2y = 21 →
  32. 32.5x + 5y = −60 and 4x − 5y = 33 →
  33. 33.2x − y = 4 and 2x − 6y = −6 →
  34. 34.6x + y = 50 and x + 6y = 20 →
  35. 35.6x + 7y = −29 and 7x + 6y = −36 →
  36. 36.5x − 3y = 32 and 6x + 4y = 46 →
  37. 37.7x + 6y = −105 and 6x + 7y = −103 →
  38. 38.6x + 4y = 56 and 6x + 3y = 51 →
  39. 39.3x − y = 16 and 2x + 2y = 32 →
  40. 40.2x − y = −15 and 2x − 6y = −30 →

Answer key

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

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