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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 305 · 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 = −41 and 6x − 6y = −18 →
  2. 2.3x + 4y = −50 and 4x + 2y = −40 →
  3. 3.5x + 7y = 44 and 7x + 5y = 52 →
  4. 4.2x + 6y = 40 and 5x + 6y = 37 →
  5. 5.4x + 6y = 32 and 6x + 4y = 38 →
  6. 6.x − y = −5 and 6x + 2y = 34 →
  7. 7.2x + y = −1 and 5x + 2y = −4 →
  8. 8.3x + 4y = −20 and x − 6y = 8 →
  9. 9.3x + 5y = −13 and 5x + 3y = −27 →
  10. 10.8x + 3y = −1 and 3x + 8y = 34 →
  11. 11.x + 2y = 15 and 2x + y = 18 →
  12. 12.x + 3y = −20 and 2x + 5y = −33 →
  13. 13.x + 4y = 30 and x − 3y = −33 →
  14. 14.3x + 5y = 28 and x − y = −12 →
  15. 15.2x + 6y = 20 and x + 2y = 9 →
  16. 16.6x + 3y = −36 and 2x + 2y = −10 →
  17. 17.4x − 6y = 44 and 5x + 4y = −14 →
  18. 18.4x + 3y = −18 and 6x − 5y = −8 →
  19. 19.3x + 5y = 33 and 2x − y = −17 →
  20. 20.x + 2y = 2 and x − 3y = 17 →
  21. 21.8x + 9y = 76 and 9x + 8y = 77 →
  22. 22.4x − 3y = −40 and 6x − 2y = −40 →
  23. 23.2x − 4y = −26 and x + 2y = 11 →
  24. 24.3x + 2y = 20 and x − y = −5 →
  25. 25.3x + 8y = 85 and 8x + 3y = 80 →
  26. 26.x + 6y = −47 and 6x + 2y = −10 →
  27. 27.2x + y = 7 and x − 2y = 1 →
  28. 28.5x − 4y = −29 and 4x + 2y = −18 →
  29. 29.6x + 2y = 58 and 2x + 6y = 62 →
  30. 30.2x + y = −11 and 3x − y = −19 →
  31. 31.7x + 2y = 41 and 2x + 7y = 31 →
  32. 32.3x + 7y = −24 and 7x + 3y = 24 →
  33. 33.5x + 2y = 24 and 6x + y = 33 →
  34. 34.3x + 6y = 81 and 6x − 6y = 0 →
  35. 35.4x + 8y = 64 and 8x + 4y = 44 →
  36. 36.4x + 2y = −22 and 4x + y = −15 →
  37. 37.3x + 2y = 39 and 2x + 3y = 36 →
  38. 38.3x − 5y = −17 and 6x + y = 43 →
  39. 39.5x − 4y = −27 and 5x + 4y = −3 →
  40. 40.8x + 3y = 19 and 3x + 8y = 69 →

Answer key

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

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