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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 490 · 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 + 3y = −17 and 5x − y = 0 →
  2. 2.3x + 3y = 12 and 6x − 3y = 6 →
  3. 3.3x + 2y = −13 and 4x − y = −21 →
  4. 4.2x − y = 16 and 6x + 4y = 62 →
  5. 5.3x − y = 21 and 4x + y = 35 →
  6. 6.5x − y = 7 and 6x + 4y = 24 →
  7. 7.4x − 6y = −44 and 3x − 6y = −36 →
  8. 8.3x + 4y = −39 and 3x − 5y = 42 →
  9. 9.3x + 6y = −30 and 2x + y = −17 →
  10. 10.3x − y = 1 and x + 5y = 11 →
  11. 11.x − y = 9 and 5x + 4y = 27 →
  12. 12.2x + 8y = −20 and 8x + 2y = 10 →
  13. 13.3x − 2y = −28 and 2x − y = −18 →
  14. 14.x + y = 0 and 4x + 2y = −14 →
  15. 15.3x + 6y = 6 and 6x + 3y = −15 →
  16. 16.3x − 5y = −13 and 2x − 4y = −12 →
  17. 17.4x + y = −7 and 5x − 6y = −45 →
  18. 18.x + 3y = −24 and 2x + 5y = −42 →
  19. 19.3x + y = −7 and x − 4y = −37 →
  20. 20.3x − y = −18 and 2x + 3y = −1 →
  21. 21.x + 2y = −9 and x + 6y = −41 →
  22. 22.5x − 5y = 0 and 4x + 5y = 18 →
  23. 23.9x + y = −66 and x + 9y = 46 →
  24. 24.5x + 2y = 44 and 4x + 5y = 59 →
  25. 25.2x + 6y = −18 and 6x + 2y = −22 →
  26. 26.3x − 4y = −4 and 4x − 4y = 0 →
  27. 27.2x + 6y = 16 and 4x + 6y = 14 →
  28. 28.5x + 3y = 44 and 3x + 5y = 36 →
  29. 29.3x + 8y = 7 and 8x + 3y = 37 →
  30. 30.x − 6y = −27 and 5x − 5y = −10 →
  31. 31.3x + 4y = −63 and x + 4y = −45 →
  32. 32.8x + y = 26 and x + 8y = 19 →
  33. 33.3x − 2y = 1 and 3x + 5y = 8 →
  34. 34.6x − 6y = 30 and 6x + 2y = 62 →
  35. 35.x − y = 1 and 3x + 3y = 45 →
  36. 36.6x − 6y = −90 and x + 2y = 3 →
  37. 37.4x + 3y = 56 and 2x + 4y = 48 →
  38. 38.6x − 4y = −50 and x + y = −10 →
  39. 39.6x + y = −55 and x + 3y = −12 →
  40. 40.6x + 3y = −45 and 2x + 6y = −10 →

Answer key

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

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