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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 6 · 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 + 4y = 48 and x + y = 10 →
  2. 2.x + 7y = −68 and 7x + y = −44 →
  3. 3.5x + 3y = −23 and 5x − 4y = 19 →
  4. 4.5x + 5y = 55 and x + 6y = 26 →
  5. 5.6x + y = 38 and x + 6y = 18 →
  6. 6.4x + 4y = 28 and 4x − 5y = −53 →
  7. 7.2x − 5y = −17 and 2x − 6y = −24 →
  8. 8.4x + 5y = 37 and 2x + y = 17 →
  9. 9.5x − 6y = 4 and x − 4y = −16 →
  10. 10.8x + 9y = 3 and 9x + 8y = 14 →
  11. 11.2x + 3y = 24 and 3x + 2y = 26 →
  12. 12.2x − 6y = −26 and 2x − 4y = −16 →
  13. 13.3x − 5y = −23 and 2x − 3y = −13 →
  14. 14.x + 2y = −23 and 2x + y = −19 →
  15. 15.9x + y = 49 and x + 9y = −39 →
  16. 16.6x − 5y = 48 and 5x − y = 21 →
  17. 17.2x + 2y = 10 and 3x − 4y = 1 →
  18. 18.3x + 4y = 19 and 2x + 2y = 10 →
  19. 19.9x + 2y = 90 and 2x + 9y = 97 →
  20. 20.x + 2y = 12 and 5x − 6y = 12 →
  21. 21.5x + y = −28 and 6x − 4y = −70 →
  22. 22.9x + 2y = 37 and 2x + 9y = 51 →
  23. 23.3x + 2y = 31 and 2x + 3y = 34 →
  24. 24.3x + 3y = 9 and 4x − 3y = 26 →
  25. 25.3x + 3y = −6 and 6x − 5y = 32 →
  26. 26.3x + 6y = 72 and 4x − 4y = 0 →
  27. 27.8x + 3y = 12 and 3x + 8y = −23 →
  28. 28.x − y = −4 and x + y = −2 →
  29. 29.3x + 4y = −17 and 6x − 4y = −46 →
  30. 30.3x + 5y = −17 and x + 6y = −23 →
  31. 31.4x + 3y = 5 and 5x + 6y = −14 →
  32. 32.x + 4y = −5 and 2x + 3y = 5 →
  33. 33.x − 6y = 12 and 6x + 3y = −45 →
  34. 34.4x + 3y = −8 and 6x + 3y = −18 →
  35. 35.5x + 4y = 26 and x + 5y = 22 →
  36. 36.2x + y = 22 and x + 2y = 20 →
  37. 37.2x − 5y = 35 and 3x + 2y = 5 →
  38. 38.4x − 3y = 9 and 3x − 3y = 6 →
  39. 39.2x − y = 17 and x − 2y = 19 →
  40. 40.4x − 5y = 53 and 6x − 3y = 57 →

Answer key

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

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