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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 325 · 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. 1.8x + y = −61 and x + 8y = 16 →
  2. 2.x + 9y = −17 and 9x + y = −73 →
  3. 3.3x + 3y = −30 and 2x + y = −19 →
  4. 4.3x − 3y = 0 and 4x + 3y = 63 →
  5. 5.4x − 5y = −18 and x − 2y = −6 →
  6. 6.2x + 3y = 16 and x + 5y = 15 →
  7. 7.x + 4y = −4 and 5x − 2y = −42 →
  8. 8.6x + 2y = 22 and 2x + 2y = 14 →
  9. 9.2x − 4y = −32 and 6x − 6y = −42 →
  10. 10.2x + 3y = 15 and 3x − 5y = −6 →
  11. 11.3x + 6y = 69 and 2x + 2y = 28 →
  12. 12.4x − 2y = 2 and 3x + 4y = −26 →
  13. 13.8x + y = 47 and x + 8y = 61 →
  14. 14.9x + 3y = 90 and 3x + 9y = 102 →
  15. 15.2x − y = −1 and 2x − 4y = −22 →
  16. 16.x + 6y = 21 and x − 2y = −11 →
  17. 17.5x − 5y = −15 and 3x − 4y = −15 →
  18. 18.5x + y = 26 and 3x − y = 14 →
  19. 19.8x + 5y = 65 and 5x + 8y = 65 →
  20. 20.2x + 6y = 24 and 6x + 2y = 40 →
  21. 21.3x − y = 11 and 3x − 4y = 35 →
  22. 22.4x + 4y = 32 and 3x + 5y = 42 →
  23. 23.3x + 4y = −6 and x + 2y = −6 →
  24. 24.8x + 2y = −60 and 2x + 8y = 30 →
  25. 25.6x + 6y = 24 and x + 3y = 6 →
  26. 26.4x + 3y = 10 and 2x + 3y = 8 →
  27. 27.6x + 4y = 60 and 3x − 5y = −12 →
  28. 28.5x + 2y = 23 and 2x + 5y = 47 →
  29. 29.5x + y = −21 and 3x + 6y = 36 →
  30. 30.2x + 6y = 52 and 6x + 2y = 44 →
  31. 31.5x + 4y = 21 and 4x + 5y = 6 →
  32. 32.2x + 2y = 12 and 2x − 5y = 5 →
  33. 33.3x + 9y = −36 and 9x + 3y = 36 →
  34. 34.2x + 2y = 18 and x − 4y = −26 →
  35. 35.4x − 6y = −6 and 5x − y = 38 →
  36. 36.6x + y = −40 and x + 6y = 5 →
  37. 37.8x + y = −75 and x + 8y = −33 →
  38. 38.x − 2y = 11 and 6x + 6y = −24 →
  39. 39.3x − 5y = 26 and 2x − y = 15 →
  40. 40.x + 2y = −8 and 2x + y = −7 →

Answer key

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

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