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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 48 · 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. 1.5x + 2y = −4 and x + 4y = −26 →
  2. 2.4x + 7y = −11 and 7x + 4y = 22 →
  3. 3.2x + 5y = 14 and 5x + 2y = −7 →
  4. 4.3x + 7y = 72 and 7x + 3y = 48 →
  5. 5.4x − 6y = −4 and 4x − 2y = 20 →
  6. 6.2x + 5y = 18 and x + 6y = 23 →
  7. 7.2x + 6y = 28 and 6x − 3y = −21 →
  8. 8.5x + 3y = 33 and 4x + 4y = 20 →
  9. 9.2x + 5y = 17 and 5x + 2y = 32 →
  10. 10.x + 5y = 26 and 5x + 2y = −31 →
  11. 11.6x − 3y = 36 and 3x + 5y = 44 →
  12. 12.x − y = −8 and 5x + y = 14 →
  13. 13.5x + 5y = 60 and 5x + y = 48 →
  14. 14.7x + 3y = 29 and 3x + 7y = −39 →
  15. 15.6x + 5y = 43 and x − 4y = −17 →
  16. 16.5x + 8y = 65 and 8x + 5y = 65 →
  17. 17.4x + y = −35 and 6x − 5y = −33 →
  18. 18.x + 5y = 42 and 5x + y = 18 →
  19. 19.6x + 2y = 4 and 4x + y = 1 →
  20. 20.5x + 9y = 63 and 9x + 5y = 91 →
  21. 21.3x − 6y = −6 and x + 5y = 12 →
  22. 22.6x − y = 35 and 4x − y = 23 →
  23. 23.x − 4y = 10 and 6x + y = 35 →
  24. 24.6x + 3y = 21 and 3x + 6y = −3 →
  25. 25.3x + 4y = −14 and 2x − 4y = 24 →
  26. 26.9x + 5y = 71 and 5x + 9y = 83 →
  27. 27.x + 6y = −15 and x + y = −10 →
  28. 28.7x + 3y = 63 and 3x + 7y = 67 →
  29. 29.7x + 9y = 144 and 9x + 7y = 144 →
  30. 30.5x + 5y = −35 and 5x − y = −17 →
  31. 31.2x + 4y = −4 and 2x − 5y = −22 →
  32. 32.4x − 2y = 40 and 2x + 2y = 8 →
  33. 33.3x + 4y = −29 and 4x + 3y = −20 →
  34. 34.3x + 4y = 16 and 2x + 2y = 10 →
  35. 35.3x + 5y = 11 and 5x + 3y = 13 →
  36. 36.9x + 8y = 118 and 8x + 9y = 120 →
  37. 37.x + 3y = 17 and 3x + y = 11 →
  38. 38.3x + 6y = −63 and 5x + y = −51 →
  39. 39.2x + 8y = −42 and 8x + 2y = 12 →
  40. 40.5x + y = −8 and 6x + y = −10 →

Answer key

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

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