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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 244 · 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.x + 2y = 14 and 2x + y = 1 →
  2. 2.6x + 3y = 12 and 5x + 6y = 17 →
  3. 3.5x − y = −46 and 2x − 4y = −22 →
  4. 4.x + 7y = −7 and 7x + y = 47 →
  5. 5.6x + 2y = 18 and 4x + 2y = 10 →
  6. 6.6x + y = 38 and 5x + 5y = 40 →
  7. 7.2x + 8y = −46 and 8x + 2y = 56 →
  8. 8.x − 4y = 16 and 4x + 4y = 4 →
  9. 9.2x + 8y = −28 and 8x + 2y = 38 →
  10. 10.5x + 2y = 29 and x + 3y = −2 →
  11. 11.5x + 3y = −9 and 3x + 5y = −31 →
  12. 12.5x − y = 29 and 4x + y = 34 →
  13. 13.5x + 3y = 6 and 3x + 5y = −6 →
  14. 14.3x + 2y = 36 and 2x + 3y = 39 →
  15. 15.6x − 5y = −35 and 6x + 5y = −25 →
  16. 16.4x + 5y = 40 and 6x − 3y = 18 →
  17. 17.2x + 3y = −29 and 2x − 6y = 16 →
  18. 18.3x + 5y = 10 and 6x + 6y = 0 →
  19. 19.8x + y = −38 and x + 8y = 11 →
  20. 20.2x + y = 21 and x − y = −3 →
  21. 21.6x − 3y = 9 and 5x − 4y = 9 →
  22. 22.3x + 7y = −10 and 7x + 3y = −50 →
  23. 23.x − 5y = −27 and 3x + 3y = 27 →
  24. 24.3x + 5y = −33 and 3x + 2y = −6 →
  25. 25.3x + y = 7 and x + 2y = −6 →
  26. 26.8x + 2y = −12 and 2x + 8y = 42 →
  27. 27.3x + 8y = 3 and 8x + 3y = 63 →
  28. 28.4x + 8y = 104 and 8x + 4y = 100 →
  29. 29.4x − 6y = 10 and x − 2y = 2 →
  30. 30.5x − 2y = 41 and x − 4y = 1 →
  31. 31.2x + 3y = 11 and 6x + 3y = −21 →
  32. 32.2x + 7y = 57 and 7x + 2y = −3 →
  33. 33.x + 5y = 9 and 3x + 2y = 1 →
  34. 34.2x + 3y = 24 and 2x + y = 20 →
  35. 35.x + 5y = −9 and 2x − 2y = −6 →
  36. 36.4x + y = 33 and 6x − y = 47 →
  37. 37.4x − 3y = −7 and 3x + 4y = 51 →
  38. 38.4x + 3y = 25 and 2x − 3y = −19 →
  39. 39.6x + y = 38 and x + 6y = 53 →
  40. 40.3x + 4y = −56 and 4x + 3y = −56 →

Answer key

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

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