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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 552 · 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. 1.6x + y = 29 and x − 5y = −21 →
  2. 2.4x + 5y = −53 and 5x + 4y = −46 →
  3. 3.x + y = 2 and 6x + 2y = −16 →
  4. 4.5x + 3y = 11 and 3x + 5y = −19 →
  5. 5.x − 3y = −13 and 6x + 5y = 37 →
  6. 6.6x + 2y = 12 and 4x − 4y = 24 →
  7. 7.2x + 3y = 8 and x − 2y = −10 →
  8. 8.6x + 2y = −58 and 2x + 6y = −30 →
  9. 9.3x − y = 13 and x + 4y = 39 →
  10. 10.4x + 5y = 33 and 5x + 4y = 21 →
  11. 11.5x + 3y = 36 and 2x − 3y = 6 →
  12. 12.x + 6y = −8 and 4x + 3y = 10 →
  13. 13.3x + 5y = 16 and 5x − 5y = 40 →
  14. 14.x − 5y = 7 and 2x − 3y = −7 →
  15. 15.4x + y = 7 and x + 4y = −17 →
  16. 16.4x + y = 28 and x + 4y = −8 →
  17. 17.4x − 2y = 12 and x − 5y = −33 →
  18. 18.x + 6y = 15 and 2x + 3y = 21 →
  19. 19.3x + 3y = 33 and 4x − 6y = −46 →
  20. 20.8x + 2y = −6 and 2x + 8y = 36 →
  21. 21.7x + 4y = −41 and 4x + 7y = −14 →
  22. 22.x + 9y = 66 and 9x + y = 34 →
  23. 23.6x + 5y = 47 and 5x + 6y = 41 →
  24. 24.3x + 4y = 19 and x + 4y = 9 →
  25. 25.4x + 6y = 64 and 6x + 2y = 54 →
  26. 26.6x − 5y = 34 and 5x + y = 18 →
  27. 27.x − y = 6 and 2x + 4y = −12 →
  28. 28.4x + 2y = 24 and 2x + 4y = 0 →
  29. 29.7x + 5y = −81 and 5x + 7y = −75 →
  30. 30.4x − 3y = 3 and 2x − 2y = 4 →
  31. 31.4x − 5y = −18 and x + y = 9 →
  32. 32.x + y = 8 and 4x + 5y = 37 →
  33. 33.4x − 3y = −44 and x + 6y = 16 →
  34. 34.5x − y = 16 and 3x + y = 16 →
  35. 35.4x − 6y = 38 and 2x + 5y = −53 →
  36. 36.9x + 6y = 87 and 6x + 9y = 93 →
  37. 37.x − y = −1 and 2x + 5y = 47 →
  38. 38.3x + 4y = −23 and x + 3y = −21 →
  39. 39.5x + y = 47 and 3x + 6y = 39 →
  40. 40.2x + 2y = 0 and 5x − 5y = 80 →

Answer key

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

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