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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 934 · 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. 1.5x + 6y = 1 and x + 6y = 29 →
  2. 2.x + 3y = 23 and 2x − 2y = −2 →
  3. 3.x − 2y = 3 and 2x − y = 12 →
  4. 4.5x + 2y = 11 and 2x + 4y = −2 →
  5. 5.5x + y = −51 and x + 6y = −45 →
  6. 6.x − y = 1 and 3x − 6y = −6 →
  7. 7.6x + 2y = 34 and 2x + 5y = 33 →
  8. 8.2x + 6y = −10 and 2x + y = 5 →
  9. 9.2x − 4y = 0 and 4x + 4y = −12 →
  10. 10.4x + 2y = −10 and 4x + 3y = −3 →
  11. 11.x + 6y = −31 and 5x − 3y = 10 →
  12. 12.9x + 4y = −34 and 4x + 9y = 21 →
  13. 13.4x + 6y = −4 and 6x + 4y = 24 →
  14. 14.2x + 4y = 38 and 2x + 5y = 47 →
  15. 15.x + 5y = 8 and 4x + 6y = 18 →
  16. 16.3x + 6y = −18 and 2x + 2y = −14 →
  17. 17.3x + y = 14 and x + 3y = 10 →
  18. 18.2x + 3y = 22 and 2x − 5y = 6 →
  19. 19.2x + 5y = 24 and 5x + 2y = 18 →
  20. 20.x − 3y = 35 and 2x − 5y = 61 →
  21. 21.2x + 4y = −24 and 4x + 2y = −6 →
  22. 22.2x + y = 22 and 6x − 6y = 30 →
  23. 23.6x + 2y = −12 and 2x + 6y = 28 →
  24. 24.4x − 3y = −3 and 6x − y = 27 →
  25. 25.6x + 6y = 24 and 3x + 5y = 28 →
  26. 26.x + y = −4 and 4x + 6y = −12 →
  27. 27.4x + 5y = 41 and 2x + y = 7 →
  28. 28.5x − 5y = −50 and x + 2y = 5 →
  29. 29.x + 6y = −33 and 6x − 5y = 48 →
  30. 30.3x − 2y = −27 and 2x − 3y = −28 →
  31. 31.x + 3y = 9 and 4x + y = −8 →
  32. 32.2x − 5y = −38 and 5x − 2y = −11 →
  33. 33.x + 5y = 14 and 2x − 3y = −11 →
  34. 34.5x + 3y = 29 and x + 5y = 19 →
  35. 35.3x + y = 16 and 6x − 5y = −17 →
  36. 36.2x + y = 15 and x + y = 8 →
  37. 37.6x − y = 10 and 4x + 5y = 18 →
  38. 38.5x − y = −3 and 3x − 2y = −13 →
  39. 39.5x + y = 34 and x + y = 2 →
  40. 40.2x + y = 12 and x + 2y = 0 →

Answer key

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

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