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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 550 · 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. 1.5x + 2y = −22 and x + 2y = 2 →
  2. 2.x + 9y = −56 and 9x + y = −24 →
  3. 3.5x − 5y = −55 and 3x + 6y = 39 →
  4. 4.5x + 8y = −5 and 8x + 5y = 31 →
  5. 5.6x + 4y = 50 and 2x − 6y = −20 →
  6. 6.x − 6y = 34 and 3x − y = 17 →
  7. 7.2x + 2y = −32 and x + 3y = −30 →
  8. 8.x + 3y = −14 and 3x + y = −2 →
  9. 9.4x + 3y = 14 and 5x − 2y = −17 →
  10. 10.x − y = −9 and 2x − 4y = −34 →
  11. 11.2x − 3y = −15 and 6x − y = −21 →
  12. 12.3x + 7y = 11 and 7x + 3y = −1 →
  13. 13.3x + y = 16 and 3x + 3y = 18 →
  14. 14.4x − 6y = −28 and 2x + 6y = 40 →
  15. 15.4x + 5y = −59 and 5x + 4y = −58 →
  16. 16.4x − y = 19 and 5x + 3y = 62 →
  17. 17.7x + y = 3 and x + 7y = −27 →
  18. 18.4x − 2y = −6 and 2x − 2y = −2 →
  19. 19.8x + 5y = 86 and 5x + 8y = 83 →
  20. 20.3x + 2y = 43 and 2x + 3y = 42 →
  21. 21.x + 2y = 11 and 2x + y = 16 →
  22. 22.2x + 4y = 2 and 4x + 2y = 10 →
  23. 23.2x + 7y = 21 and 7x + 2y = 51 →
  24. 24.6x − 2y = 32 and 4x + 6y = −30 →
  25. 25.5x + 2y = 38 and 2x + 5y = 53 →
  26. 26.x + 4y = 31 and 6x + 6y = 24 →
  27. 27.5x + y = 1 and 2x + y = −5 →
  28. 28.9x + 5y = 67 and 5x + 9y = 31 →
  29. 29.x + 2y = 9 and 2x + y = 6 →
  30. 30.5x + 3y = −5 and 3x + 2y = −4 →
  31. 31.6x − 6y = −12 and 5x + 2y = 11 →
  32. 32.9x + 7y = 44 and 7x + 9y = 52 →
  33. 33.3x − 6y = 39 and x − 3y = 20 →
  34. 34.3x − 2y = 30 and 3x − 6y = 54 →
  35. 35.x + 7y = 20 and 7x + y = −52 →
  36. 36.5x − 6y = −79 and x − 6y = −59 →
  37. 37.7x + y = 64 and x + 7y = 64 →
  38. 38.2x + y = 15 and x + 2y = 15 →
  39. 39.2x + 5y = 31 and 5x + y = −3 →
  40. 40.5x + 2y = −7 and 4x + y = −5 →

Answer key

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

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