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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 472 · 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 + 3y = 10 and 3x + y = −2 →
  2. 2.x + y = 5 and 3x − 4y = −48 →
  3. 3.2x + 6y = −32 and 6x + 2y = 32 →
  4. 4.4x + 4y = 4 and 4x − y = −21 →
  5. 5.2x + 4y = 2 and x + 4y = 9 →
  6. 6.4x − 3y = −11 and x − 2y = 6 →
  7. 7.6x + 4y = 14 and 4x + 6y = 16 →
  8. 8.4x + 5y = 48 and 5x + 4y = 51 →
  9. 9.x + 3y = −25 and 5x + y = −41 →
  10. 10.5x + 3y = −7 and 2x − 6y = −10 →
  11. 11.5x + 3y = −13 and x + 2y = 10 →
  12. 12.2x − 2y = −26 and 3x + 5y = −7 →
  13. 13.2x + 2y = 32 and 3x − 4y = −8 →
  14. 14.x − 5y = 35 and 4x + 6y = −16 →
  15. 15.x − 3y = −19 and 6x − 5y = −10 →
  16. 16.5x + 9y = −44 and 9x + 5y = −12 →
  17. 17.3x − 6y = −36 and 3x − y = 4 →
  18. 18.2x + y = 18 and 5x + 2y = 43 →
  19. 19.x + 5y = 11 and x − 3y = −5 →
  20. 20.3x − y = 6 and 3x + y = 12 →
  21. 21.5x − 5y = 10 and 2x + 5y = 53 →
  22. 22.4x + 2y = 38 and 2x + 4y = 40 →
  23. 23.6x + 5y = 15 and 3x − y = −24 →
  24. 24.3x + 2y = −27 and 2x + 3y = −28 →
  25. 25.x + 2y = −7 and 5x + 6y = −39 →
  26. 26.6x + 4y = 28 and x + 2y = 10 →
  27. 27.6x + 9y = −66 and 9x + 6y = −39 →
  28. 28.x + 4y = 16 and 4x + 5y = 42 →
  29. 29.6x + 4y = 22 and 3x + 6y = 39 →
  30. 30.3x + 4y = 34 and 4x + y = 28 →
  31. 31.6x + 2y = 10 and 6x − 2y = 26 →
  32. 32.4x − y = 30 and 3x + 3y = 0 →
  33. 33.4x − 6y = −72 and 2x + 4y = 6 →
  34. 34.x + 2y = 16 and 2x + y = 20 →
  35. 35.x − y = 2 and 4x − y = 23 →
  36. 36.3x + 2y = 22 and 3x − 5y = −34 →
  37. 37.6x + y = 23 and 3x + y = 11 →
  38. 38.9x + 6y = 102 and 6x + 9y = 93 →
  39. 39.4x − 4y = −12 and 4x + 4y = 20 →
  40. 40.5x − 5y = −85 and x + 2y = 10 →

Answer key

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

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