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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 177 · 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 − y = 8 and 4x − 4y = 16 →
  2. 2.4x − 6y = 12 and 2x + 2y = 16 →
  3. 3.5x + 5y = −30 and x − 5y = 48 →
  4. 4.7x + 4y = −61 and 4x + 7y = −49 →
  5. 5.x + 2y = −15 and 2x + y = −12 →
  6. 6.x + 2y = −1 and 2x + y = −8 →
  7. 7.6x − 5y = 37 and 5x + 2y = 37 →
  8. 8.6x + y = −52 and 6x + 5y = −44 →
  9. 9.4x + 3y = 30 and 3x + 6y = 30 →
  10. 10.4x + y = 3 and x + 4y = −33 →
  11. 11.7x + 5y = 33 and 5x + 7y = 27 →
  12. 12.x + 2y = −16 and 4x + 3y = −29 →
  13. 13.9x + 6y = 81 and 6x + 9y = 69 →
  14. 14.x − y = −2 and x + 3y = −10 →
  15. 15.5x + 3y = 0 and 6x − 4y = 38 →
  16. 16.6x + y = −63 and 2x + 2y = −36 →
  17. 17.5x + 6y = 74 and 3x + 2y = 30 →
  18. 18.5x + y = 24 and 5x − y = 16 →
  19. 19.5x − y = 3 and 3x − 4y = 29 →
  20. 20.3x + 6y = −3 and 4x − 4y = −16 →
  21. 21.4x + 5y = 54 and 5x + 4y = 54 →
  22. 22.x + 6y = −50 and x + y = −15 →
  23. 23.x − 5y = −47 and 3x − 5y = −51 →
  24. 24.3x + 5y = −53 and 2x + 4y = −40 →
  25. 25.x + 5y = 37 and 3x + 6y = 30 →
  26. 26.6x + 4y = 10 and 6x − 3y = 66 →
  27. 27.3x + 3y = 21 and 2x + 4y = 12 →
  28. 28.6x + y = 38 and 2x + y = 14 →
  29. 29.5x − 5y = −60 and 2x + y = −15 →
  30. 30.3x + 5y = −17 and 5x + 3y = −39 →
  31. 31.6x + 3y = −12 and x + y = −5 →
  32. 32.x + 5y = 1 and 5x − 5y = 35 →
  33. 33.6x + 2y = 44 and 6x + 6y = 24 →
  34. 34.6x + 2y = 20 and 6x − 2y = 4 →
  35. 35.4x + 6y = 54 and 5x + 5y = 50 →
  36. 36.x + 6y = 16 and 5x + 5y = 30 →
  37. 37.6x + 3y = 6 and 2x − 6y = −26 →
  38. 38.6x + 6y = −12 and 3x + 4y = −1 →
  39. 39.6x + 4y = 70 and x + y = 13 →
  40. 40.5x + 2y = −39 and 4x + 4y = −24 →

Answer key

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

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