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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 420 · 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. 1.5x + 7y = 32 and 7x + 5y = 40 →
  2. 2.2x + 3y = 13 and 5x + 2y = 27 →
  3. 3.9x + 5y = 57 and 5x + 9y = 69 →
  4. 4.5x + 3y = −18 and x + 4y = 27 →
  5. 5.5x + 7y = −4 and 7x + 5y = 28 →
  6. 6.3x + y = 26 and x + 3y = 14 →
  7. 7.9x + 2y = 68 and 2x + 9y = −2 →
  8. 8.2x + 6y = 34 and x + 6y = 29 →
  9. 9.3x + 3y = 27 and x + 4y = 33 →
  10. 10.5x + 5y = −65 and 4x − 2y = −10 →
  11. 11.5x + 9y = 55 and 9x + 5y = 43 →
  12. 12.3x + 6y = 72 and 3x − 5y = −27 →
  13. 13.4x + 3y = −30 and 3x + 4y = −19 →
  14. 14.2x + y = 0 and x + 2y = 3 →
  15. 15.8x + 6y = −80 and 6x + 8y = −88 →
  16. 16.3x + 6y = −15 and 6x + 3y = −3 →
  17. 17.4x + 4y = −24 and 5x + 6y = −29 →
  18. 18.3x − 2y = 42 and 5x + y = 31 →
  19. 19.6x + 2y = 60 and 2x + y = 23 →
  20. 20.2x + 4y = 18 and 4x + 4y = 28 →
  21. 21.5x + 9y = 34 and 9x + 5y = 50 →
  22. 22.x − 4y = 14 and 5x − 2y = 16 →
  23. 23.9x + 7y = 102 and 7x + 9y = 90 →
  24. 24.3x − 3y = 12 and 2x − 4y = 2 →
  25. 25.9x + 7y = 67 and 7x + 9y = 77 →
  26. 26.4x − 6y = −60 and 4x − 4y = −48 →
  27. 27.2x − y = −3 and x − 6y = −40 →
  28. 28.x − 3y = −14 and 6x + 5y = 77 →
  29. 29.8x + 4y = 52 and 4x + 8y = 32 →
  30. 30.8x + 6y = 30 and 6x + 8y = 26 →
  31. 31.x + y = 4 and 6x + 2y = 16 →
  32. 32.8x + y = 60 and x + 8y = 39 →
  33. 33.x − 4y = −33 and 3x + 6y = 9 →
  34. 34.5x + 2y = 47 and 4x + 2y = 40 →
  35. 35.4x + y = 20 and 6x + y = 32 →
  36. 36.6x + 2y = 32 and x + 5y = 38 →
  37. 37.3x + 4y = 41 and 5x − 5y = −25 →
  38. 38.2x + y = −1 and 4x − y = 25 →
  39. 39.4x + 2y = −2 and 6x + 4y = −12 →
  40. 40.x + 3y = −4 and 3x + y = −20 →

Answer key

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

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