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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 145 · 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 + 5y = −20 and 3x + 2y = −15 →
  2. 2.x + 2y = 15 and 2x + y = 6 →
  3. 3.5x + y = −1 and 4x − y = −8 →
  4. 4.2x + y = 17 and x + 3y = 16 →
  5. 5.6x + 3y = 3 and 6x − y = 7 →
  6. 6.2x + 2y = −14 and 3x + 6y = −27 →
  7. 7.x − 6y = 58 and 5x − y = 29 →
  8. 8.5x + y = 23 and 5x + 3y = 39 →
  9. 9.6x + 2y = 60 and 4x + 2y = 42 →
  10. 10.6x − 3y = −63 and 5x + 2y = −12 →
  11. 11.8x + 4y = −4 and 4x + 8y = 4 →
  12. 12.x − y = −5 and x + y = 9 →
  13. 13.4x + y = 29 and 5x + 6y = 22 →
  14. 14.4x + 5y = −51 and 5x + 4y = −48 →
  15. 15.4x + 3y = −14 and 6x + 6y = −30 →
  16. 16.9x + 3y = −21 and 3x + 9y = −39 →
  17. 17.6x + 4y = −36 and 2x + 4y = −28 →
  18. 18.9x + 7y = 77 and 7x + 9y = 67 →
  19. 19.6x − 6y = 36 and x + 2y = 0 →
  20. 20.9x + 2y = −71 and 2x + 9y = 27 →
  21. 21.3x + 2y = 45 and 2x + y = 27 →
  22. 22.5x + 4y = 76 and x − y = −1 →
  23. 23.4x + 2y = −38 and 6x + 2y = −54 →
  24. 24.8x + 2y = 52 and 2x + 8y = 58 →
  25. 25.x + 2y = 14 and x − y = −10 →
  26. 26.x + 5y = −7 and 2x + y = 4 →
  27. 27.5x + 6y = 44 and 6x + 6y = 48 →
  28. 28.4x + 2y = 0 and x + 3y = −5 →
  29. 29.3x + 2y = −1 and 2x + 6y = −10 →
  30. 30.4x − 4y = 0 and 4x + 4y = −24 →
  31. 31.x + 7y = 48 and 7x + y = 48 →
  32. 32.7x + 5y = 45 and 5x + 7y = 39 →
  33. 33.3x + 2y = 20 and 3x + 6y = 36 →
  34. 34.x − 5y = −26 and 2x + 4y = 32 →
  35. 35.4x + 5y = −38 and 5x + 2y = −39 →
  36. 36.3x − 6y = −45 and 6x − y = −13 →
  37. 37.2x + 4y = 26 and 3x + 5y = 34 →
  38. 38.3x + y = −5 and x + 3y = −7 →
  39. 39.5x + 2y = 29 and 2x + 5y = −1 →
  40. 40.x + 2y = −9 and 4x + 6y = −32 →

Answer key

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

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