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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 367 · 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.x + 2y = 9 and 5x + 3y = −4 →
  2. 2.6x + 9y = −96 and 9x + 6y = −84 →
  3. 3.3x − 2y = 32 and 6x + 4y = 32 →
  4. 4.8x + 2y = 48 and 2x + 8y = −48 →
  5. 5.5x + y = 3 and x + 5y = −33 →
  6. 6.3x + 4y = 31 and 4x + 3y = 39 →
  7. 7.3x + 9y = 15 and 9x + 3y = 21 →
  8. 8.4x + 7y = 60 and 7x + 4y = 72 →
  9. 9.x + 6y = 42 and 6x + y = 42 →
  10. 10.6x − 3y = 63 and 3x + 2y = 0 →
  11. 11.9x + 7y = 80 and 7x + 9y = 80 →
  12. 12.3x + 6y = 24 and 4x + y = 11 →
  13. 13.6x + y = −9 and x + 6y = 16 →
  14. 14.2x + 5y = −16 and x + 3y = −11 →
  15. 15.5x + 2y = 35 and 6x + 6y = 24 →
  16. 16.5x + 3y = −10 and 3x + 5y = −22 →
  17. 17.5x + 5y = −25 and 4x + 6y = −18 →
  18. 18.3x + 2y = −26 and 2x + 3y = −19 →
  19. 19.3x + 4y = −13 and 4x + 3y = −22 →
  20. 20.3x + 8y = 29 and 8x + 3y = 59 →
  21. 21.x − 6y = 26 and x + 2y = −6 →
  22. 22.x + 4y = 26 and 4x + y = 29 →
  23. 23.6x + 4y = 34 and 2x + 3y = 18 →
  24. 24.4x + 3y = 4 and 3x + 4y = −4 →
  25. 25.3x − 6y = 33 and 5x + 5y = −80 →
  26. 26.4x + y = 29 and 4x + 2y = 38 →
  27. 27.4x + y = −17 and x + 4y = 22 →
  28. 28.4x + 9y = −51 and 9x + 4y = −1 →
  29. 29.x − 3y = −14 and 5x + y = 42 →
  30. 30.9x + 8y = −128 and 8x + 9y = −127 →
  31. 31.5x + 8y = 8 and 8x + 5y = 44 →
  32. 32.2x + 2y = −4 and 5x − 2y = 46 →
  33. 33.x + 5y = 14 and x − 5y = −6 →
  34. 34.x + 4y = 10 and x − 6y = −20 →
  35. 35.2x + 2y = 14 and 3x + 6y = 48 →
  36. 36.3x + 3y = 9 and x + 4y = 18 →
  37. 37.6x − y = 49 and 4x + 2y = 46 →
  38. 38.8x + 9y = 63 and 9x + 8y = 73 →
  39. 39.x − 3y = −12 and 2x + 5y = −2 →
  40. 40.x + 4y = 34 and 2x + 3y = 23 →

Answer key

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

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