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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 786 · 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 − 2y = −16 and x + 6y = 55 →
  2. 2.x + y = 1 and x + 2y = −1 →
  3. 3.3x + 6y = −9 and 4x + 3y = −17 →
  4. 4.4x + 2y = 52 and 2x + 4y = 50 →
  5. 5.x + 4y = −19 and 4x + y = −31 →
  6. 6.6x + y = −26 and 5x + 4y = −9 →
  7. 7.2x − 2y = −2 and 5x − 3y = 5 →
  8. 8.6x − y = 20 and 5x + 2y = 28 →
  9. 9.2x + 7y = −43 and 7x + 2y = −38 →
  10. 10.4x + 3y = 21 and 3x + 4y = 21 →
  11. 11.4x − 2y = 22 and x − 6y = 22 →
  12. 12.2x − 4y = 14 and 5x − y = 17 →
  13. 13.2x − y = −9 and 2x + 4y = 26 →
  14. 14.3x + y = 19 and 6x − 2y = 34 →
  15. 15.2x + 5y = 21 and 3x + 5y = 29 →
  16. 16.2x + 6y = 26 and 6x + 2y = 46 →
  17. 17.2x + 3y = 21 and 2x + 5y = 23 →
  18. 18.2x − 2y = −10 and 5x + 5y = 65 →
  19. 19.4x + 5y = 4 and 4x + y = −28 →
  20. 20.4x + 3y = −17 and 3x + 4y = −4 →
  21. 21.3x − 6y = 9 and 5x + 4y = 43 →
  22. 22.7x + 2y = 4 and 2x + 7y = −31 →
  23. 23.8x + 5y = 107 and 5x + 8y = 101 →
  24. 24.6x − 4y = −40 and 3x − y = −16 →
  25. 25.x + 3y = 23 and 6x + 3y = 48 →
  26. 26.6x + 4y = −18 and 5x + 4y = −21 →
  27. 27.x + 3y = 26 and 3x + y = 22 →
  28. 28.3x + y = −6 and x + 3y = −26 →
  29. 29.2x − 3y = 23 and 4x + 3y = −17 →
  30. 30.4x + 8y = 16 and 8x + 4y = 20 →
  31. 31.6x − 5y = 32 and 5x + 6y = 47 →
  32. 32.8x + 9y = 7 and 9x + 8y = −7 →
  33. 33.3x + 3y = 6 and 3x − 3y = 36 →
  34. 34.2x + 4y = 16 and 5x − 2y = −32 →
  35. 35.4x − 3y = −31 and x + 6y = 26 →
  36. 36.x + 5y = −29 and 3x + 6y = −33 →
  37. 37.6x + 9y = 99 and 9x + 6y = 111 →
  38. 38.2x + 6y = 38 and 2x − y = 3 →
  39. 39.9x + 3y = −102 and 3x + 9y = −90 →
  40. 40.x − 3y = −22 and 2x + 6y = 52 →

Answer key

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

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