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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 496 · 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. 1.4x − 3y = −1 and 5x + 3y = −8 →
  2. 2.x − 5y = −8 and 6x + y = 45 →
  3. 3.7x + 8y = −20 and 8x + 7y = −25 →
  4. 4.6x + 4y = 46 and 4x + 6y = 34 →
  5. 5.4x + 6y = 44 and 6x − y = 46 →
  6. 6.3x − 2y = −24 and 6x − 5y = −57 →
  7. 7.5x + 4y = 8 and x + 2y = −8 →
  8. 8.2x + y = −20 and x + 2y = −19 →
  9. 9.5x + 5y = −60 and 3x + 4y = −45 →
  10. 10.9x + y = 50 and x + 9y = 50 →
  11. 11.5x + 4y = −21 and x + 4y = −17 →
  12. 12.7x + 4y = −29 and 4x + 7y = −26 →
  13. 13.x + y = 10 and 2x − 5y = −43 →
  14. 14.5x + 5y = −10 and 5x − 3y = 38 →
  15. 15.4x + 9y = 62 and 9x + 4y = 42 →
  16. 16.x − 4y = −29 and x + 3y = 34 →
  17. 17.3x + 6y = −54 and 6x − 3y = 12 →
  18. 18.3x − 3y = −9 and 3x − 2y = −2 →
  19. 19.6x + 3y = 24 and 3x + 6y = −6 →
  20. 20.3x − 3y = −3 and 2x + 5y = 19 →
  21. 21.3x + y = −23 and 4x + y = −32 →
  22. 22.2x + y = 8 and 5x + y = 14 →
  23. 23.6x + 6y = 0 and 4x − 4y = −72 →
  24. 24.2x + 6y = 20 and 6x + 2y = −20 →
  25. 25.4x + y = −40 and 3x + 3y = −48 →
  26. 26.3x + y = −6 and 3x − 4y = −36 →
  27. 27.x + 6y = 26 and 3x + 4y = 36 →
  28. 28.6x − y = 2 and 6x + y = −14 →
  29. 29.6x + 4y = −10 and 5x + 4y = −5 →
  30. 30.2x + 2y = −10 and 2x + 3y = −12 →
  31. 31.9x + 7y = 30 and 7x + 9y = 34 →
  32. 32.2x − 3y = −13 and x − 3y = −8 →
  33. 33.6x + 3y = 21 and 4x − y = 35 →
  34. 34.4x + 5y = −1 and x − 5y = 6 →
  35. 35.2x − 4y = 2 and 4x + 6y = 32 →
  36. 36.4x + y = 14 and x + 4y = 11 →
  37. 37.x + 5y = −44 and 5x + 2y = −59 →
  38. 38.x − y = −2 and 2x − 4y = −10 →
  39. 39.x + 3y = −25 and 3x + y = −3 →
  40. 40.x + 4y = −28 and 2x − y = 25 →

Answer key

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

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