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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 36 · 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 + 4y = 3 and 3x + 4y = −7 →
  2. 2.4x + 6y = 40 and 2x + 2y = 12 →
  3. 3.4x + y = −19 and 2x − 4y = −14 →
  4. 4.5x + 6y = 29 and 6x + 5y = 15 →
  5. 5.4x + 2y = 28 and 4x + 3y = 34 →
  6. 6.8x + 9y = 29 and 9x + 8y = 39 →
  7. 7.3x + 3y = −15 and x + 6y = 15 →
  8. 8.6x − 5y = −26 and 2x − 2y = −8 →
  9. 9.x + 3y = 7 and 2x + 3y = 8 →
  10. 10.6x − 2y = 24 and x − y = −2 →
  11. 11.2x + 5y = −23 and 3x − 4y = 23 →
  12. 12.6x + 7y = −10 and 7x + 6y = −3 →
  13. 13.3x − 4y = −20 and 3x + 3y = −27 →
  14. 14.6x + 9y = −57 and 9x + 6y = −18 →
  15. 15.2x + 8y = 60 and 8x + 2y = 30 →
  16. 16.2x + 3y = 33 and 3x + 2y = 27 →
  17. 17.5x + 2y = 31 and 3x + 6y = 57 →
  18. 18.x + 4y = −10 and 4x − 2y = 14 →
  19. 19.x − 3y = −2 and x − 5y = −8 →
  20. 20.2x + 2y = −28 and 3x − 3y = 12 →
  21. 21.6x + y = 2 and 6x − 5y = −46 →
  22. 22.3x + 5y = −10 and 2x + 3y = −7 →
  23. 23.2x + 9y = 17 and 9x + 2y = 38 →
  24. 24.6x + 7y = −31 and 7x + 6y = −21 →
  25. 25.4x − 4y = −56 and x + 4y = 11 →
  26. 26.2x − 5y = −22 and 6x − 2y = −14 →
  27. 27.2x + y = 6 and x + 2y = 6 →
  28. 28.6x + 3y = 63 and 3x + 6y = 54 →
  29. 29.2x + y = −11 and 2x + 3y = −21 →
  30. 30.x − y = −13 and 3x − 4y = −43 →
  31. 31.x + 3y = 11 and 3x + 4y = 13 →
  32. 32.6x + 5y = 44 and 5x + 5y = 40 →
  33. 33.x + 5y = 14 and 5x + y = −2 →
  34. 34.2x − 3y = −24 and x + 6y = 3 →
  35. 35.x + 8y = 25 and 8x + y = −52 →
  36. 36.x + 2y = 16 and 3x + 4y = 34 →
  37. 37.x − 4y = 18 and 4x − 3y = 20 →
  38. 38.3x + 6y = 6 and 5x + 5y = 20 →
  39. 39.9x + 6y = 12 and 6x + 9y = −27 →
  40. 40.5x + y = −5 and x + 5y = 23 →

Answer key

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

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