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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 707 · 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. 1.6x + y = 32 and x + 6y = 17 →
  2. 2.x + 9y = −73 and 9x + y = −17 →
  3. 3.4x + 6y = −90 and 2x − y = −9 →
  4. 4.5x − 3y = 12 and x + y = 4 →
  5. 5.x + 3y = 25 and 5x − y = −3 →
  6. 6.x + 6y = −60 and 6x + 5y = −81 →
  7. 7.6x − 6y = −84 and 5x + y = −22 →
  8. 8.x + 8y = 50 and 8x + y = 22 →
  9. 9.x + 2y = −3 and 5x + y = 21 →
  10. 10.5x + 3y = −20 and 3x + 5y = 4 →
  11. 11.2x + 6y = −40 and 4x − 3y = 40 →
  12. 12.5x + 9y = 62 and 9x + 5y = 78 →
  13. 13.6x + 2y = −2 and 4x + 5y = 17 →
  14. 14.3x + 7y = 58 and 7x + 3y = 42 →
  15. 15.6x + y = 5 and x + 6y = −5 →
  16. 16.2x + y = 15 and 3x + 5y = 40 →
  17. 17.5x + 2y = −23 and 6x − 5y = −72 →
  18. 18.2x − 2y = 14 and x + 4y = 17 →
  19. 19.7x + 8y = −41 and 8x + 7y = −49 →
  20. 20.6x + 7y = 44 and 7x + 6y = 47 →
  21. 21.x + 3y = −24 and 3x + y = 0 →
  22. 22.6x + 3y = 42 and 3x + 6y = 3 →
  23. 23.3x + 4y = 23 and 4x + y = 35 →
  24. 24.4x + y = −21 and x + 4y = −39 →
  25. 25.4x − 4y = −52 and 6x + 2y = −22 →
  26. 26.6x + y = 55 and x + 6y = 50 →
  27. 27.7x + 3y = 32 and 3x + 7y = 48 →
  28. 28.4x − 3y = 11 and 3x + y = 5 →
  29. 29.9x + 5y = −31 and 5x + 9y = −67 →
  30. 30.3x + 6y = −9 and 3x + 3y = −12 →
  31. 31.6x + 5y = 48 and 4x − 5y = −18 →
  32. 32.5x + 7y = −32 and 7x + 5y = −40 →
  33. 33.6x + y = 17 and x + 6y = 32 →
  34. 34.x + 4y = −11 and x + y = −8 →
  35. 35.6x + 4y = 14 and 4x + 6y = 6 →
  36. 36.4x + 4y = −48 and 5x + 2y = −33 →
  37. 37.3x − 6y = 15 and 4x + y = −25 →
  38. 38.8x + 3y = −19 and 3x + 8y = −69 →
  39. 39.2x + 2y = 8 and 4x − 4y = −48 →
  40. 40.2x + 5y = −6 and 5x + 2y = −36 →

Answer key

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

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