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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 39 · 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. 1.2x + 6y = 56 and 4x + 3y = 31 →
  2. 2.6x + 2y = 56 and 2x + 6y = 24 →
  3. 3.6x + 7y = −68 and 7x + 6y = −62 →
  4. 4.3x − y = 16 and 3x + 4y = −4 →
  5. 5.8x + 5y = −4 and 5x + 8y = 17 →
  6. 6.2x + y = 8 and x + 4y = −17 →
  7. 7.6x + 3y = 6 and x + 2y = 7 →
  8. 8.2x + 7y = −19 and 7x + 2y = 46 →
  9. 9.5x + 4y = −3 and 2x + 2y = −4 →
  10. 10.2x − 3y = 11 and 4x + 4y = 12 →
  11. 11.6x + 9y = −6 and 9x + 6y = 21 →
  12. 12.3x + 5y = −39 and 2x + 3y = −23 →
  13. 13.4x − 3y = 33 and 5x − y = 33 →
  14. 14.4x − y = 4 and 6x − 4y = −4 →
  15. 15.7x + 2y = −19 and 2x + 7y = −44 →
  16. 16.5x − 4y = 28 and 6x − 5y = 33 →
  17. 17.x − 4y = −27 and 4x + 2y = 54 →
  18. 18.2x − 4y = −46 and x + 4y = 31 →
  19. 19.4x − 6y = 54 and 6x + y = 11 →
  20. 20.2x + 3y = 0 and 3x + 4y = 1 →
  21. 21.5x + y = 24 and x + 4y = 20 →
  22. 22.5x + 6y = 3 and 5x + 3y = −21 →
  23. 23.4x + 3y = −18 and 5x − 6y = −3 →
  24. 24.4x + 3y = 20 and x + 3y = 14 →
  25. 25.4x − 6y = 40 and 4x + y = −2 →
  26. 26.5x + 5y = 20 and x + 6y = 14 →
  27. 27.6x + 2y = 28 and x − 4y = −17 →
  28. 28.3x − 2y = 5 and 3x + y = 29 →
  29. 29.2x − 2y = −2 and 4x − 3y = 3 →
  30. 30.6x + y = 50 and x + 6y = 20 →
  31. 31.3x + 9y = −60 and 9x + 3y = −36 →
  32. 32.6x + 5y = 47 and 5x + 6y = 41 →
  33. 33.5x − 6y = 10 and 3x + 2y = 34 →
  34. 34.2x + 6y = 8 and 5x − 6y = −1 →
  35. 35.4x + 3y = 53 and x − 5y = −27 →
  36. 36.x + 6y = 8 and 2x + 5y = 9 →
  37. 37.3x − 4y = −40 and 3x + y = −20 →
  38. 38.2x − 3y = −29 and 5x + 2y = −6 →
  39. 39.2x + 9y = 40 and 9x + 2y = 26 →
  40. 40.6x − 3y = −45 and 2x + 3y = −19 →

Answer key

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

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