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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 563 · 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 − 5y = 81 and x + 5y = −36 →
  2. 2.5x − 6y = 21 and 2x − 2y = 10 →
  3. 3.3x + 4y = 15 and 4x + 3y = −1 →
  4. 4.6x − 3y = 27 and x + 2y = −3 →
  5. 5.6x − 3y = 18 and 6x − 2y = 20 →
  6. 6.5x + 4y = 22 and 5x + y = 13 →
  7. 7.4x + 8y = −28 and 8x + 4y = −68 →
  8. 8.5x + 3y = −31 and 2x − 6y = 38 →
  9. 9.6x + y = −23 and 2x − 4y = 14 →
  10. 10.2x − 4y = 6 and 6x + y = −47 →
  11. 11.6x + 4y = 22 and 4x + 5y = 24 →
  12. 12.6x + 3y = −6 and 3x + 6y = −21 →
  13. 13.2x − 5y = 6 and 2x + 5y = 26 →
  14. 14.6x − y = 43 and x + 5y = 2 →
  15. 15.6x + 5y = −1 and 5x + 6y = −10 →
  16. 16.4x + 2y = 26 and 3x + y = 16 →
  17. 17.3x + y = 17 and x + 4y = 35 →
  18. 18.3x − y = 20 and 2x + y = 5 →
  19. 19.6x + 2y = 20 and 3x − 5y = 58 →
  20. 20.x + 6y = −15 and 6x + y = 15 →
  21. 21.6x − 6y = −12 and 4x − 3y = −11 →
  22. 22.4x + y = −18 and 6x + 3y = −36 →
  23. 23.3x + 6y = −9 and 6x − y = 47 →
  24. 24.4x + 2y = 4 and 3x − y = 23 →
  25. 25.5x + 3y = −34 and 6x + 3y = −39 →
  26. 26.2x + 4y = −42 and 3x − 4y = 27 →
  27. 27.x + 3y = 19 and 3x + y = 1 →
  28. 28.6x + 4y = 34 and 3x + 4y = 19 →
  29. 29.x + 6y = 3 and 6x − 5y = −64 →
  30. 30.4x − 6y = −12 and 3x + y = −20 →
  31. 31.8x + 9y = 136 and 9x + 8y = 136 →
  32. 32.2x + 9y = 73 and 9x + 2y = 59 →
  33. 33.x + 4y = 38 and 4x − 5y = −16 →
  34. 34.8x + 6y = −14 and 6x + 8y = −28 →
  35. 35.x + 4y = −17 and 3x + 2y = −11 →
  36. 36.5x + 5y = 80 and 5x + 3y = 66 →
  37. 37.6x + 3y = 69 and 6x + 6y = 90 →
  38. 38.x + 5y = −30 and 5x + y = 18 →
  39. 39.6x − 5y = 5 and 5x − y = −18 →
  40. 40.6x + 4y = 6 and 4x + 2y = 10 →

Answer key

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

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