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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 933 · 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 6x − 3y = −39 →
  2. 2.2x + 3y = 12 and 3x + 2y = 13 →
  3. 3.x + 2y = 1 and 2x + y = 8 →
  4. 4.3x − 5y = 52 and 2x − y = 16 →
  5. 5.4x + 4y = −8 and 5x + 2y = −7 →
  6. 6.x − 2y = −5 and 5x − 6y = −13 →
  7. 7.6x + 2y = 58 and 2x − 6y = −14 →
  8. 8.2x + 2y = −28 and 5x + 3y = −60 →
  9. 9.x + 2y = 9 and 2x − 5y = −9 →
  10. 10.7x + 9y = 47 and 9x + 7y = 65 →
  11. 11.9x + 2y = 78 and 2x + 9y = 43 →
  12. 12.4x − 3y = −29 and x + 5y = 33 →
  13. 13.6x + 7y = 85 and 7x + 6y = 84 →
  14. 14.2x + 5y = 19 and 5x + 2y = 16 →
  15. 15.4x − 2y = 42 and 2x − 2y = 30 →
  16. 16.x − 4y = −26 and 3x + 5y = 58 →
  17. 17.2x + 3y = 1 and 3x + 2y = 4 →
  18. 18.4x − y = −13 and 3x + 3y = −6 →
  19. 19.2x + y = −22 and 2x + 5y = −46 →
  20. 20.6x + 2y = −22 and 2x + 6y = −34 →
  21. 21.9x + 3y = 78 and 3x + 9y = 42 →
  22. 22.6x + 3y = 12 and 5x − 2y = 1 →
  23. 23.3x + 5y = −45 and 5x + 3y = −43 →
  24. 24.4x + y = −14 and 5x + 4y = −34 →
  25. 25.x − y = 3 and 5x + 3y = 63 →
  26. 26.x + 7y = 64 and 7x + y = 64 →
  27. 27.4x − y = −17 and 5x − 5y = −40 →
  28. 28.4x + 8y = 48 and 8x + 4y = 72 →
  29. 29.2x + 5y = 48 and 5x + 2y = 57 →
  30. 30.2x − 2y = −24 and x + 2y = 0 →
  31. 31.3x + 4y = 1 and 5x + 2y = −3 →
  32. 32.8x + 2y = 12 and 2x + 8y = 18 →
  33. 33.5x + y = −9 and 4x + 2y = −6 →
  34. 34.2x − 5y = −3 and x − 4y = −6 →
  35. 35.2x + 4y = −12 and 4x + 4y = −20 →
  36. 36.3x + 4y = 48 and 5x + 2y = 38 →
  37. 37.3x + 6y = 6 and 6x + 2y = −38 →
  38. 38.5x + y = −8 and 2x − 6y = −16 →
  39. 39.5x + 5y = 5 and 2x − 4y = −22 →
  40. 40.2x + 5y = −16 and 4x − y = 12 →

Answer key

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

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