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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 127 · 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. 1.2x + 6y = 18 and 6x + 2y = −10 →
  2. 2.4x + 8y = −80 and 8x + 4y = −52 →
  3. 3.5x + 5y = 80 and x + 2y = 25 →
  4. 4.5x + y = 40 and 2x + y = 13 →
  5. 5.4x − 5y = −8 and 4x − y = 8 →
  6. 6.6x + 2y = 34 and 3x − y = 1 →
  7. 7.5x − 4y = −68 and 3x + 5y = 11 →
  8. 8.x − 5y = −21 and 5x − 5y = −5 →
  9. 9.4x + y = −7 and x + 4y = 32 →
  10. 10.6x + 2y = 28 and 3x + 3y = 24 →
  11. 11.3x + 3y = −12 and 3x + 2y = −6 →
  12. 12.3x + 5y = −12 and 5x + 3y = −4 →
  13. 13.3x + 6y = −33 and 6x + 3y = −21 →
  14. 14.7x + 2y = 10 and 2x + 7y = −55 →
  15. 15.x + 3y = −10 and 4x + 6y = −16 →
  16. 16.x + 4y = 15 and 6x − 6y = 0 →
  17. 17.5x − 2y = 22 and 5x + 3y = −8 →
  18. 18.5x + 2y = 63 and 2x + 5y = 63 →
  19. 19.4x + y = 44 and 3x + 4y = 59 →
  20. 20.3x + 9y = −45 and 9x + 3y = −39 →
  21. 21.5x + 6y = 58 and 6x + 5y = 52 →
  22. 22.x + 3y = 9 and 4x + 6y = 6 →
  23. 23.3x + 4y = 7 and 4x − y = −35 →
  24. 24.8x + 9y = 48 and 9x + 8y = 37 →
  25. 25.5x + 6y = 4 and 6x + 5y = 7 →
  26. 26.6x + 4y = 14 and 3x + 3y = 9 →
  27. 27.2x + 5y = 44 and 5x − 3y = 17 →
  28. 28.6x + 8y = −54 and 8x + 6y = −44 →
  29. 29.x + 4y = −29 and x + y = −14 →
  30. 30.4x − 2y = 42 and x + 2y = 3 →
  31. 31.8x + 2y = 32 and 2x + 8y = 38 →
  32. 32.9x + 2y = 4 and 2x + 9y = −59 →
  33. 33.9x + y = 44 and x + 9y = 76 →
  34. 34.2x − 4y = −14 and 2x + 3y = −7 →
  35. 35.8x + 5y = −23 and 5x + 8y = −29 →
  36. 36.5x + 3y = −13 and x + y = −5 →
  37. 37.3x + 2y = 1 and 2x + 3y = −6 →
  38. 38.5x − 4y = −1 and 2x + 6y = 30 →
  39. 39.5x + 2y = 44 and 3x + 2y = 28 →
  40. 40.6x − 3y = −69 and 5x + 3y = −30 →

Answer key

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

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