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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 942 · 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. 1.6x − 4y = −72 and 2x + 4y = 24 →
  2. 2.2x + 6y = 44 and 4x + 2y = −2 →
  3. 3.2x + y = 7 and x + 2y = 5 →
  4. 4.3x + 2y = 1 and 2x + 3y = −1 →
  5. 5.2x − y = −14 and 4x + 4y = 8 →
  6. 6.4x − y = −23 and 4x − 2y = −26 →
  7. 7.6x + 4y = 36 and 2x − 6y = −10 →
  8. 8.3x − 3y = 9 and 6x − y = 23 →
  9. 9.5x + y = −3 and x + 4y = −31 →
  10. 10.5x + y = 10 and 4x + 2y = 14 →
  11. 11.3x + 6y = −12 and x − 4y = −16 →
  12. 12.6x + 4y = 44 and 4x + 6y = 36 →
  13. 13.4x + 2y = 40 and x + 2y = 16 →
  14. 14.x − 6y = −2 and 4x + y = 17 →
  15. 15.5x + 6y = −44 and 6x + 6y = −42 →
  16. 16.5x + 9y = 3 and 9x + 5y = −17 →
  17. 17.4x − 2y = −28 and 4x + 6y = −12 →
  18. 18.8x + 2y = 36 and 2x + 8y = −6 →
  19. 19.x − 4y = −27 and 5x + 5y = 65 →
  20. 20.2x − y = −8 and 3x + 3y = −3 →
  21. 21.2x + 8y = 74 and 8x + 2y = 26 →
  22. 22.2x + 5y = 52 and 2x + 2y = 28 →
  23. 23.5x + y = 14 and 3x − 3y = 12 →
  24. 24.3x + 2y = −1 and x − 2y = −3 →
  25. 25.7x + 9y = 42 and 9x + 7y = 22 →
  26. 26.5x + 2y = 19 and 5x − y = −2 →
  27. 27.6x + 7y = −40 and 7x + 6y = −38 →
  28. 28.6x + 5y = 31 and 6x + y = 11 →
  29. 29.2x − 3y = −6 and x − 2y = −6 →
  30. 30.6x + 2y = 26 and 3x + 3y = 15 →
  31. 31.2x − 6y = 8 and 4x − 5y = 23 →
  32. 32.2x − 4y = −30 and 4x − 4y = −28 →
  33. 33.4x + 2y = 22 and 2x + 4y = 38 →
  34. 34.6x + 9y = 27 and 9x + 6y = 33 →
  35. 35.5x + 6y = 51 and 6x + 5y = 48 →
  36. 36.5x + 2y = 21 and 3x + y = 13 →
  37. 37.x + 5y = −18 and 5x + y = 30 →
  38. 38.2x + 3y = 6 and 4x − 5y = −76 →
  39. 39.3x + 9y = −63 and 9x + 3y = 3 →
  40. 40.5x − 4y = 3 and 6x + 4y = 74 →

Answer key

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

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