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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 573 · 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. 1.6x + 3y = −33 and 3x + 6y = −12 →
  2. 2.2x + 9y = 74 and 9x + 2y = 25 →
  3. 3.4x − 6y = 26 and 6x + 5y = 53 →
  4. 4.7x + y = −38 and x + 7y = 22 →
  5. 5.4x + y = 41 and 2x + 6y = 70 →
  6. 6.2x + 4y = −4 and 2x + 3y = −5 →
  7. 7.5x + 3y = −4 and 5x + 4y = −2 →
  8. 8.7x + 8y = 65 and 8x + 7y = 55 →
  9. 9.2x + 5y = −37 and x + 2y = −16 →
  10. 10.3x + 4y = 11 and 4x + 3y = −4 →
  11. 11.4x + 5y = −8 and 3x + 2y = 8 →
  12. 12.6x − y = −25 and x + 2y = −2 →
  13. 13.2x + 3y = −36 and 6x + 6y = −90 →
  14. 14.3x + y = 12 and x + 3y = −4 →
  15. 15.9x + 3y = 57 and 3x + 9y = 75 →
  16. 16.9x + y = −25 and x + 9y = 15 →
  17. 17.x − 2y = −4 and 2x + y = −3 →
  18. 18.2x + 3y = 22 and 3x + 3y = 21 →
  19. 19.6x − 5y = 75 and x + y = −4 →
  20. 20.6x + 3y = −9 and 3x + 6y = −9 →
  21. 21.6x + 3y = 6 and 6x + 2y = 10 →
  22. 22.3x − 5y = −13 and 6x + 4y = −40 →
  23. 23.2x + 2y = 28 and 4x − y = 26 →
  24. 24.9x + y = 42 and x + 9y = 58 →
  25. 25.8x + 3y = −20 and 3x + 8y = −35 →
  26. 26.x + 6y = 51 and x + 4y = 37 →
  27. 27.2x + 7y = −6 and 7x + 2y = 24 →
  28. 28.x + 3y = 7 and x + 2y = 2 →
  29. 29.9x + y = 19 and x + 9y = 11 →
  30. 30.x + 5y = 35 and x + 3y = 23 →
  31. 31.9x + 8y = 75 and 8x + 9y = 78 →
  32. 32.5x + 2y = 53 and 3x − 3y = −6 →
  33. 33.4x + y = −31 and x + 4y = 11 →
  34. 34.6x + 5y = 1 and x − 6y = −34 →
  35. 35.4x + 6y = 18 and x − 2y = 1 →
  36. 36.x − 5y = 2 and 4x − 2y = −28 →
  37. 37.3x + 6y = −39 and 6x + 3y = −42 →
  38. 38.8x + y = −69 and x + 8y = 15 →
  39. 39.x − 2y = −6 and x + 6y = 50 →
  40. 40.7x + 3y = 24 and 3x + 7y = −24 →

Answer key

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

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