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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 800 · 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 + 5y = 63 and 4x + 6y = 90 →
  2. 2.5x + 3y = −1 and 3x + 5y = 9 →
  3. 3.x + 6y = −36 and 5x + 5y = −5 →
  4. 4.4x + 6y = −38 and 3x − 3y = −21 →
  5. 5.6x + 8y = 20 and 8x + 6y = 8 →
  6. 6.x + 9y = 42 and 9x + y = 58 →
  7. 7.9x + 4y = −79 and 4x + 9y = −64 →
  8. 8.4x + 2y = 38 and x + 5y = 41 →
  9. 9.7x + 9y = 39 and 9x + 7y = 9 →
  10. 10.6x + y = 40 and 5x + 3y = 16 →
  11. 11.3x − 5y = −18 and 5x − 3y = −14 →
  12. 12.6x + 3y = 24 and x + 4y = −17 →
  13. 13.5x + 3y = −4 and 5x − 3y = 44 →
  14. 14.x + 4y = 25 and 4x + y = 40 →
  15. 15.4x + 9y = 60 and 9x + 4y = 5 →
  16. 16.2x + 8y = 56 and 8x + 2y = 44 →
  17. 17.6x + 3y = 69 and 3x − 5y = −11 →
  18. 18.x + 6y = −9 and x − y = 12 →
  19. 19.3x + 4y = −2 and 4x + 3y = 9 →
  20. 20.2x + y = 13 and x + 2y = 2 →
  21. 21.4x − 3y = −14 and 4x + 3y = −2 →
  22. 22.2x + 2y = 4 and x + 4y = −1 →
  23. 23.6x − 2y = −22 and 5x − 2y = −19 →
  24. 24.5x + 3y = 33 and 6x + 3y = 39 →
  25. 25.x + 3y = −15 and 2x + 2y = −2 →
  26. 26.8x + y = 40 and x + 8y = 68 →
  27. 27.3x + y = −12 and 2x + 4y = 12 →
  28. 28.x − 4y = 32 and x + 6y = −38 →
  29. 29.5x − y = −4 and 3x + y = −4 →
  30. 30.x − 2y = 5 and 3x − 2y = −5 →
  31. 31.3x − 4y = 7 and x + 3y = 24 →
  32. 32.4x + 3y = 43 and 3x + 4y = 41 →
  33. 33.x + 2y = −3 and 5x − 3y = −41 →
  34. 34.3x − 3y = −3 and 4x − 3y = 4 →
  35. 35.5x + 6y = 67 and 2x − 2y = −4 →
  36. 36.2x − 3y = −3 and 5x + 6y = 60 →
  37. 37.5x − 3y = −31 and 3x − 4y = −34 →
  38. 38.2x + 9y = 55 and 9x + 2y = 55 →
  39. 39.2x + 6y = 30 and 5x + 4y = 42 →
  40. 40.7x + 9y = 126 and 9x + 7y = 130 →

Answer key

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

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