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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 988 · 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. 1.4x − 6y = −28 and x + y = 3 →
  2. 2.6x + 9y = −30 and 9x + 6y = 0 →
  3. 3.5x + y = 31 and x + 5y = 35 →
  4. 4.5x + 9y = 69 and 9x + 5y = 57 →
  5. 5.3x + 2y = −18 and 2x + 3y = −7 →
  6. 6.4x + 2y = 44 and 2x + 4y = 46 →
  7. 7.7x + 9y = −89 and 9x + 7y = −87 →
  8. 8.9x + 7y = −107 and 7x + 9y = −101 →
  9. 9.5x + 8y = −12 and 8x + 5y = −27 →
  10. 10.3x − 4y = −29 and 2x − 4y = −26 →
  11. 11.x − 2y = −16 and 5x + y = 19 →
  12. 12.5x − y = 0 and 6x + 4y = 26 →
  13. 13.6x − y = −3 and 2x − 3y = 23 →
  14. 14.5x − 3y = −33 and 2x + 3y = −9 →
  15. 15.4x + 5y = 8 and 5x + 4y = −8 →
  16. 16.7x + 4y = 55 and 4x + 7y = 22 →
  17. 17.4x + 7y = 50 and 7x + 4y = 38 →
  18. 18.x + 6y = 29 and 4x − 6y = −64 →
  19. 19.x + 3y = −15 and 3x + y = −13 →
  20. 20.x + 8y = 68 and 8x + y = −23 →
  21. 21.5x + 7y = −67 and 7x + 5y = −65 →
  22. 22.4x + 8y = −20 and 8x + 4y = 44 →
  23. 23.2x − 5y = −36 and 3x + 5y = 46 →
  24. 24.5x + 3y = 69 and 4x − 2y = 20 →
  25. 25.3x − 5y = 6 and 6x − 4y = 30 →
  26. 26.6x + y = 28 and x − 4y = 13 →
  27. 27.x + 2y = 2 and x − 6y = −14 →
  28. 28.5x + 6y = −29 and 6x + 5y = −37 →
  29. 29.6x + 6y = 78 and 2x + 6y = 62 →
  30. 30.6x + 8y = 50 and 8x + 6y = 62 →
  31. 31.7x + 2y = 29 and 2x + 7y = −11 →
  32. 32.2x − 5y = 7 and 2x − 2y = 4 →
  33. 33.6x − 3y = −45 and 2x + y = −13 →
  34. 34.2x + 7y = 24 and 7x + 2y = 39 →
  35. 35.4x + y = 6 and 5x − 2y = 27 →
  36. 36.4x + 6y = −20 and 4x − 4y = 0 →
  37. 37.x − y = −11 and 2x + y = −7 →
  38. 38.3x + y = 14 and x − 6y = −27 →
  39. 39.2x + y = −17 and x + 2y = −13 →
  40. 40.4x − 4y = −28 and 3x + y = 11 →

Answer key

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

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