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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 34 · 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. 1.3x − 4y = −36 and x − 4y = −20 →
  2. 2.4x − y = −26 and 5x − y = −32 →
  3. 3.x + 3y = 22 and 4x + 5y = 25 →
  4. 4.3x − 3y = 9 and 3x + y = 13 →
  5. 5.4x − 4y = 16 and 6x + 5y = −53 →
  6. 6.x + y = 2 and 5x + 2y = 1 →
  7. 7.2x + y = −12 and x + 2y = −3 →
  8. 8.6x + 2y = −20 and 5x + 4y = −19 →
  9. 9.8x + 4y = 36 and 4x + 8y = 48 →
  10. 10.4x + 5y = 33 and 4x − 6y = −22 →
  11. 11.2x + y = 23 and 4x + 5y = 61 →
  12. 12.3x + y = 16 and x − 6y = −39 →
  13. 13.3x + 8y = −16 and 8x + 3y = −61 →
  14. 14.8x + 2y = −46 and 2x + 8y = −4 →
  15. 15.8x + 9y = −11 and 9x + 8y = −6 →
  16. 16.4x + 5y = −7 and 2x − 4y = 16 →
  17. 17.5x − 3y = −59 and 2x + 5y = 26 →
  18. 18.5x + 2y = −6 and x + 6y = 38 →
  19. 19.2x − y = −4 and 3x + y = −26 →
  20. 20.4x + 3y = 7 and 4x + 4y = 8 →
  21. 21.8x + 3y = 54 and 3x + 8y = −21 →
  22. 22.4x + 3y = 24 and 2x + 5y = 26 →
  23. 23.5x − 5y = 15 and 6x − 2y = 10 →
  24. 24.x + 7y = −31 and 7x + y = −25 →
  25. 25.9x + 2y = 48 and 2x + 9y = −15 →
  26. 26.2x + 4y = 0 and 4x + 2y = −18 →
  27. 27.2x + 3y = 20 and x − 3y = 1 →
  28. 28.6x + y = 16 and x + 6y = −44 →
  29. 29.x − 4y = −29 and 2x − 2y = −16 →
  30. 30.3x + 7y = −7 and 7x + 3y = 37 →
  31. 31.3x + 6y = 33 and x + 4y = 13 →
  32. 32.x + 6y = 4 and 2x − y = −18 →
  33. 33.x + 4y = −35 and 6x − 3y = 33 →
  34. 34.7x + y = 23 and x + 7y = 65 →
  35. 35.3x + y = 0 and x − 3y = −20 →
  36. 36.2x + 5y = −17 and 2x + 4y = −10 →
  37. 37.8x + y = 13 and x + 8y = 41 →
  38. 38.x + 3y = 23 and 2x + 3y = 31 →
  39. 39.8x + 9y = 32 and 9x + 8y = 19 →
  40. 40.x + 4y = −5 and 6x + y = 16 →

Answer key

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

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