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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 125 · 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 + 5y = 30 and 5x + 5y = 10 →
  2. 2.5x + 3y = 19 and 2x + 4y = 2 →
  3. 3.3x + y = −4 and 4x − 4y = 32 →
  4. 4.3x + 2y = −37 and 6x + y = −50 →
  5. 5.x − 4y = 23 and 2x − 4y = 22 →
  6. 6.x − 6y = −10 and 4x + 5y = 18 →
  7. 7.3x + 5y = −30 and 5x + 3y = −34 →
  8. 8.2x + 9y = 30 and 9x + 2y = −19 →
  9. 9.5x + 5y = 45 and 6x − y = 33 →
  10. 10.5x − y = 0 and 6x + 5y = 31 →
  11. 11.6x + 5y = −2 and 5x + 6y = −9 →
  12. 12.6x + 2y = 64 and 2x + 3y = 40 →
  13. 13.x + 8y = 28 and 8x + y = 35 →
  14. 14.6x + 6y = 42 and 2x + 5y = 26 →
  15. 15.6x − 5y = 15 and 2x − 2y = 8 →
  16. 16.2x − y = 12 and 5x + 3y = 63 →
  17. 17.6x − 5y = −56 and x + 5y = 14 →
  18. 18.4x + 5y = 33 and 3x + y = 11 →
  19. 19.5x + y = 29 and x + 2y = 4 →
  20. 20.2x − 2y = 2 and 6x − y = 31 →
  21. 21.3x + 9y = −39 and 9x + 3y = −69 →
  22. 22.x − y = 4 and 3x + 4y = 26 →
  23. 23.x + 4y = 40 and x − 5y = −32 →
  24. 24.3x + 8y = −27 and 8x + 3y = −17 →
  25. 25.5x + 4y = 24 and 4x + 5y = 21 →
  26. 26.2x + 6y = 8 and 2x + y = 13 →
  27. 27.4x + 6y = 46 and x + 2y = 15 →
  28. 28.2x + 3y = 0 and 3x + 2y = 15 →
  29. 29.2x − 6y = −24 and 2x − 2y = −4 →
  30. 30.6x − y = −13 and 3x + 2y = 11 →
  31. 31.4x + 3y = −19 and 3x + 6y = −33 →
  32. 32.5x + y = 14 and 2x + 3y = 16 →
  33. 33.x − 6y = −8 and 6x − 2y = 20 →
  34. 34.3x + 9y = −33 and 9x + 3y = −3 →
  35. 35.x + 9y = −54 and 9x + y = 74 →
  36. 36.6x + y = −3 and 4x + 5y = −41 →
  37. 37.3x + 4y = −17 and x + 2y = −11 →
  38. 38.5x − 3y = 43 and 5x + 5y = −5 →
  39. 39.6x + 2y = 20 and x + 3y = −10 →
  40. 40.x + y = 6 and x + 5y = 10 →

Answer key

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

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