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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 209 · 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 = −9 and 6x − 4y = 48 →
  2. 2.6x + 4y = 38 and 5x + 3y = 29 →
  3. 3.4x + y = −28 and x + 4y = 23 →
  4. 4.7x + 2y = 44 and 2x + 7y = 19 →
  5. 5.3x + 6y = 39 and 6x + 3y = 24 →
  6. 6.6x − 6y = −18 and x − 6y = −48 →
  7. 7.2x + 4y = 44 and 4x + 2y = 40 →
  8. 8.4x + 7y = −9 and 7x + 4y = 9 →
  9. 9.5x + 2y = −42 and 2x + 5y = −21 →
  10. 10.5x − 2y = 34 and 6x + y = 51 →
  11. 11.x + 2y = 1 and 2x + y = −13 →
  12. 12.8x + 6y = −96 and 6x + 8y = −86 →
  13. 13.2x − 2y = 16 and 6x − 5y = 39 →
  14. 14.3x − 5y = −27 and 4x − 4y = −20 →
  15. 15.2x + 9y = −44 and 9x + 2y = 33 →
  16. 16.4x + 3y = 41 and 6x + y = 37 →
  17. 17.3x + 6y = 48 and 6x + 3y = 33 →
  18. 18.2x + 6y = −8 and 6x − 3y = 39 →
  19. 19.6x + y = −7 and 3x + y = −1 →
  20. 20.5x + 9y = −14 and 9x + 5y = 42 →
  21. 21.6x + y = 8 and 6x + 3y = 12 →
  22. 22.3x + 5y = −40 and 5x + 3y = −40 →
  23. 23.4x − y = −13 and 3x + 6y = 24 →
  24. 24.6x − 3y = −27 and 2x + y = 1 →
  25. 25.4x + 5y = 13 and 5x + 4y = 14 →
  26. 26.6x + 4y = 50 and 3x + 4y = 23 →
  27. 27.4x + 6y = 56 and 3x + 2y = 32 →
  28. 28.5x + 4y = −4 and 2x + 4y = −16 →
  29. 29.5x − 4y = 22 and 6x − y = 34 →
  30. 30.2x − 2y = 16 and 4x + 5y = −22 →
  31. 31.6x + 5y = 51 and 5x + 5y = 45 →
  32. 32.6x + 2y = 22 and 4x + 2y = 16 →
  33. 33.4x − 4y = 12 and 6x + 5y = 29 →
  34. 34.6x + y = −29 and 3x − 3y = −18 →
  35. 35.3x + 5y = 21 and 5x + 3y = −13 →
  36. 36.5x + y = 36 and x + 6y = 42 →
  37. 37.8x + 7y = 97 and 7x + 8y = 98 →
  38. 38.4x + 5y = 37 and 4x + y = 1 →
  39. 39.3x + 9y = 87 and 9x + 3y = 69 →
  40. 40.6x + 2y = −4 and 6x + 6y = 12 →

Answer key

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

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