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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 260 · 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 + 6y = −16 and 6x + 2y = 32 →
  2. 2.3x + 5y = 16 and 4x + 3y = 14 →
  3. 3.4x + 2y = −10 and 2x + 4y = 4 →
  4. 4.5x − y = 28 and 2x − 4y = 4 →
  5. 5.6x + 2y = 18 and 2x + 6y = −42 →
  6. 6.4x − 3y = 55 and 5x + 3y = 8 →
  7. 7.x + 3y = 15 and 3x + 4y = 35 →
  8. 8.2x + 4y = 18 and 3x + 4y = 21 →
  9. 9.3x + 5y = −23 and 3x − 6y = 54 →
  10. 10.6x + 5y = 1 and 5x − 6y = 72 →
  11. 11.x + 6y = 30 and 4x + 3y = −6 →
  12. 12.4x + 2y = 20 and 6x + 5y = 18 →
  13. 13.7x + y = −25 and x + 7y = −31 →
  14. 14.2x + 9y = −11 and 9x + 2y = 66 →
  15. 15.2x + 4y = 10 and 3x + 5y = 12 →
  16. 16.2x − 6y = 46 and 3x + 6y = −51 →
  17. 17.4x + y = −34 and 2x + 5y = −26 →
  18. 18.4x + 2y = −20 and x + 6y = 6 →
  19. 19.5x + 2y = 46 and 2x + 5y = 31 →
  20. 20.3x + 4y = −19 and 3x + 5y = −20 →
  21. 21.x + 2y = 0 and 5x + 3y = −14 →
  22. 22.2x + y = 10 and x + y = 8 →
  23. 23.8x + 3y = 19 and 3x + 8y = 14 →
  24. 24.x + 3y = 18 and 2x + 5y = 33 →
  25. 25.4x + 6y = 42 and 4x − 2y = 2 →
  26. 26.2x + 2y = 10 and 3x + 6y = 18 →
  27. 27.x + y = 5 and x + 2y = 12 →
  28. 28.4x − 4y = 0 and 4x − y = 9 →
  29. 29.8x + 3y = −36 and 3x + 8y = 14 →
  30. 30.5x − 3y = 7 and x + y = 11 →
  31. 31.x + 5y = 11 and 5x + y = −17 →
  32. 32.4x + 2y = 28 and x − 2y = 17 →
  33. 33.2x + y = 5 and x + 2y = 4 →
  34. 34.3x − y = 7 and x − y = 5 →
  35. 35.3x − 4y = 38 and 2x − 2y = 22 →
  36. 36.2x − 3y = −14 and 4x + 4y = −8 →
  37. 37.3x + 4y = −16 and 6x + 5y = −11 →
  38. 38.5x + 5y = 65 and 5x − 2y = 30 →
  39. 39.7x + 3y = 25 and 3x + 7y = 45 →
  40. 40.4x − 3y = −47 and 3x + 3y = 12 →

Answer key

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

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