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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 245 · 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. 1.4x − y = 7 and 6x + 2y = 14 →
  2. 2.3x + y = −13 and x + 4y = 25 →
  3. 3.3x + 2y = −10 and 2x + 3y = 0 →
  4. 4.5x + 4y = 24 and 4x + 5y = 12 →
  5. 5.9x + 7y = −45 and 7x + 9y = −67 →
  6. 6.2x − y = 10 and x + 5y = 16 →
  7. 7.2x − 5y = −34 and x − 5y = −37 →
  8. 8.x + 2y = 21 and 5x − 6y = −39 →
  9. 9.7x + y = 36 and x + 7y = 12 →
  10. 10.6x + 8y = 80 and 8x + 6y = 88 →
  11. 11.2x + 5y = 56 and 2x − 3y = −8 →
  12. 12.4x − y = 8 and 2x + 3y = −10 →
  13. 13.x + 5y = 24 and 5x + 5y = 0 →
  14. 14.4x + 5y = 27 and 3x + y = 1 →
  15. 15.5x + 2y = −18 and 2x + 5y = −3 →
  16. 16.9x + 2y = −67 and 2x + 9y = 45 →
  17. 17.3x + 5y = 9 and 4x − 4y = −20 →
  18. 18.3x + 6y = −18 and 2x + 6y = −22 →
  19. 19.x + 4y = 28 and 4x + 6y = 52 →
  20. 20.5x + 6y = −37 and 3x − 2y = 17 →
  21. 21.3x + 4y = 32 and 5x − 6y = −10 →
  22. 22.x − 2y = −9 and 4x + 2y = 54 →
  23. 23.3x + 5y = 22 and 4x − 2y = 12 →
  24. 24.2x + 6y = 40 and 6x + 2y = −8 →
  25. 25.x + 4y = −18 and x + y = −6 →
  26. 26.5x + 6y = −14 and 4x + 2y = 0 →
  27. 27.6x − 4y = 72 and 2x + y = 10 →
  28. 28.5x − y = −2 and x − y = −6 →
  29. 29.2x + y = 7 and x + 2y = 5 →
  30. 30.4x + 6y = 26 and 6x + 4y = 24 →
  31. 31.x + 6y = 15 and 6x + 3y = 24 →
  32. 32.2x + y = 12 and x + y = 10 →
  33. 33.3x + y = 20 and x + 3y = −12 →
  34. 34.4x − 6y = −6 and 2x + y = −7 →
  35. 35.6x + 3y = 45 and 3x + 6y = 18 →
  36. 36.6x − 3y = −21 and x + y = 10 →
  37. 37.5x + 3y = −30 and 3x + 5y = −2 →
  38. 38.6x + 3y = 21 and 5x + 5y = 20 →
  39. 39.3x + 2y = −8 and 2x + 3y = −17 →
  40. 40.6x + 7y = −31 and 7x + 6y = −34 →

Answer key

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

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