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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 665 · 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. 1.3x + 5y = −42 and 5x + 4y = −31 →
  2. 2.5x − 5y = −75 and 2x + 4y = 6 →
  3. 3.2x + 6y = 60 and x − 4y = −33 →
  4. 4.6x + 5y = −14 and 5x + 6y = −19 →
  5. 5.8x + 6y = 62 and 6x + 8y = 78 →
  6. 6.x + 2y = 2 and 6x − 6y = −78 →
  7. 7.4x + 6y = −42 and 6x − 4y = 54 →
  8. 8.6x + 3y = 33 and 6x − 2y = 28 →
  9. 9.2x − 5y = −37 and 3x + 5y = 7 →
  10. 10.x − 3y = −15 and 6x − 6y = 6 →
  11. 11.x − 5y = −32 and 2x + 3y = 14 →
  12. 12.7x + 5y = −52 and 5x + 7y = −68 →
  13. 13.6x − y = 33 and 6x + 3y = 45 →
  14. 14.6x − 4y = 52 and 2x − 2y = 22 →
  15. 15.6x + 2y = −26 and 5x + 2y = −24 →
  16. 16.3x + 4y = −46 and 3x − y = −11 →
  17. 17.3x + 5y = 53 and 2x + 5y = 47 →
  18. 18.x + 3y = 4 and x − 2y = 9 →
  19. 19.x − 2y = −19 and 4x + 3y = 1 →
  20. 20.2x − y = 11 and 6x + 5y = 73 →
  21. 21.6x + 5y = −4 and x + 4y = 12 →
  22. 22.4x + 5y = −57 and 5x + 4y = −51 →
  23. 23.2x + 3y = −15 and 6x + 6y = −18 →
  24. 24.x + 5y = −23 and 5x + y = −19 →
  25. 25.5x + 4y = 68 and 3x − 2y = 10 →
  26. 26.4x + 3y = 43 and 2x + 4y = 34 →
  27. 27.x − 3y = 7 and 5x + 4y = −41 →
  28. 28.2x + 2y = 6 and 5x + 4y = 19 →
  29. 29.6x + 9y = 126 and 9x + 6y = 129 →
  30. 30.3x + 4y = −2 and 4x + 3y = 2 →
  31. 31.7x + 9y = −19 and 9x + 7y = 3 →
  32. 32.2x + 6y = 40 and 5x + 6y = 55 →
  33. 33.2x + y = 6 and 3x − 2y = 2 →
  34. 34.x − 2y = −1 and 4x + 3y = 18 →
  35. 35.7x + 4y = 19 and 4x + 7y = 25 →
  36. 36.x − 5y = −14 and 3x + 4y = 15 →
  37. 37.6x + y = 48 and 2x − 2y = 30 →
  38. 38.x + 8y = 70 and 8x + y = −7 →
  39. 39.6x − y = 32 and 3x − 2y = 10 →
  40. 40.x − 2y = −14 and 4x − y = −21 →

Answer key

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

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