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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 258 · 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.x + 2y = 1 and x + 5y = −8 →
  2. 2.3x + 2y = −9 and 5x − 3y = 42 →
  3. 3.8x + 9y = −27 and 9x + 8y = −41 →
  4. 4.2x + 3y = 11 and 3x + 3y = 15 →
  5. 5.6x − 3y = −39 and 2x + 6y = −6 →
  6. 6.4x − 2y = −14 and 5x + y = 0 →
  7. 7.x + 6y = 8 and 6x + y = 13 →
  8. 8.x − 3y = 6 and x + 3y = 0 →
  9. 9.6x + 6y = 60 and 5x + 3y = 46 →
  10. 10.x + 9y = −48 and 9x + y = 48 →
  11. 11.x − y = 6 and 6x + 3y = 63 →
  12. 12.7x + 2y = 21 and 2x + 7y = −39 →
  13. 13.4x + 8y = 72 and 8x + 4y = 84 →
  14. 14.5x + 6y = −27 and 4x + y = 5 →
  15. 15.9x + 5y = 62 and 5x + 9y = 78 →
  16. 16.x + 5y = 33 and 5x + y = −3 →
  17. 17.4x + 3y = 29 and 3x + 4y = 34 →
  18. 18.3x + y = 15 and x + 3y = 13 →
  19. 19.7x + 6y = −50 and 6x + 7y = −41 →
  20. 20.4x − 3y = −23 and 2x − y = −13 →
  21. 21.x + 4y = 19 and 4x + 3y = 11 →
  22. 22.x + 9y = −17 and 9x + y = 7 →
  23. 23.3x + 3y = 9 and 6x + 5y = 9 →
  24. 24.x + 4y = −13 and 5x − 3y = 27 →
  25. 25.6x + y = −10 and x + 6y = 10 →
  26. 26.2x + 2y = 12 and 5x − 5y = 10 →
  27. 27.x + 2y = 10 and 2x + 2y = 8 →
  28. 28.4x + 3y = 34 and x + y = 9 →
  29. 29.x + 2y = 13 and x − 3y = −7 →
  30. 30.6x + 5y = 41 and 2x − 2y = 10 →
  31. 31.5x + y = 53 and 6x + 5y = 94 →
  32. 32.5x + 6y = −66 and x + y = −12 →
  33. 33.2x + 2y = 0 and 5x + y = −32 →
  34. 34.4x + 5y = 29 and 5x + 4y = 25 →
  35. 35.x − 4y = 35 and 5x + 4y = 7 →
  36. 36.5x + 2y = 13 and 2x + 5y = 22 →
  37. 37.x − 4y = −27 and 4x + 5y = 18 →
  38. 38.5x − 5y = −30 and 3x + 4y = −32 →
  39. 39.3x + 2y = −12 and 5x + 3y = −17 →
  40. 40.4x + 3y = 47 and 3x − y = 6 →

Answer key

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

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