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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 971 · 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.x + y = −7 and 5x + 2y = −8 →
  2. 2.3x + 9y = 108 and 9x + 3y = 108 →
  3. 3.3x + 6y = 27 and 6x + 3y = 36 →
  4. 4.2x + y = −17 and 6x + y = −41 →
  5. 5.3x + 6y = −36 and 5x + y = 12 →
  6. 6.2x + 4y = −24 and 2x + 2y = −16 →
  7. 7.6x + 3y = 9 and 2x + 2y = 4 →
  8. 8.8x + 9y = −54 and 9x + 8y = −65 →
  9. 9.4x + 5y = −5 and x + 5y = 10 →
  10. 10.3x + 5y = −62 and 2x + 2y = −32 →
  11. 11.3x + 6y = −9 and 6x + 3y = −27 →
  12. 12.x − y = −5 and x + 3y = 19 →
  13. 13.2x + 2y = 20 and 6x + 2y = 48 →
  14. 14.3x + 4y = 17 and x + 3y = 9 →
  15. 15.x + 4y = −15 and 2x + 2y = −6 →
  16. 16.2x + 5y = 36 and 5x + 2y = 48 →
  17. 17.6x + 5y = −43 and 5x + 3y = −37 →
  18. 18.5x + 3y = −1 and 4x + y = 2 →
  19. 19.x − 5y = 18 and 3x + 4y = −3 →
  20. 20.4x + y = −6 and 3x − 4y = 5 →
  21. 21.2x + 3y = 15 and 4x + y = 25 →
  22. 22.2x + 3y = −8 and 6x + 4y = −34 →
  23. 23.5x + y = 33 and 6x − y = 33 →
  24. 24.7x + 6y = 99 and 6x + 7y = 96 →
  25. 25.5x + 3y = 63 and 3x + 5y = 57 →
  26. 26.8x + 9y = −111 and 9x + 8y = −110 →
  27. 27.6x + 2y = 0 and 6x + 4y = −12 →
  28. 28.4x + 5y = −37 and 5x + 4y = −26 →
  29. 29.2x + 4y = 46 and 4x + 2y = 44 →
  30. 30.6x − y = 11 and 5x + 5y = −20 →
  31. 31.x − 3y = −20 and 6x + 4y = 56 →
  32. 32.x + 9y = −23 and 9x + y = −47 →
  33. 33.4x + 5y = 22 and 5x + 4y = 23 →
  34. 34.2x + 2y = 16 and 5x − 2y = −23 →
  35. 35.9x + y = 44 and x + 9y = 76 →
  36. 36.6x + 5y = 59 and 3x + 4y = 31 →
  37. 37.3x − 6y = 15 and 6x + y = −61 →
  38. 38.2x + 4y = 20 and 2x + 2y = 6 →
  39. 39.x + 2y = −14 and 2x + y = −4 →
  40. 40.x + 2y = 17 and 2x + y = 16 →

Answer key

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

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