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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 117 · 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 + 9y = −51 and 9x + 6y = −9 →
  2. 2.x + 4y = −43 and 4x − 2y = −10 →
  3. 3.3x + 2y = −4 and 6x + 5y = −1 →
  4. 4.4x + 2y = −20 and 2x + 4y = −4 →
  5. 5.7x + 5y = 41 and 5x + 7y = 43 →
  6. 6.7x + 4y = 11 and 4x + 7y = 11 →
  7. 7.6x + y = 14 and x + 6y = 49 →
  8. 8.3x + 3y = 30 and x + 3y = 26 →
  9. 9.2x + 4y = 10 and 5x + 3y = 39 →
  10. 10.6x + 5y = 44 and 5x + 6y = 44 →
  11. 11.2x − y = 1 and 6x − 2y = 8 →
  12. 12.2x + 5y = −12 and 5x + 2y = 33 →
  13. 13.2x + y = −11 and x + 2y = 2 →
  14. 14.4x + y = 14 and 3x + 3y = 24 →
  15. 15.5x + 4y = 19 and 3x − 3y = 33 →
  16. 16.6x + 7y = 33 and 7x + 6y = 32 →
  17. 17.5x + y = −38 and x + 5y = −46 →
  18. 18.x + 3y = 4 and 6x + 3y = 39 →
  19. 19.x + 7y = −19 and 7x + y = 11 →
  20. 20.6x + 2y = −48 and 2x + 6y = 0 →
  21. 21.x + 3y = −17 and 3x + y = −3 →
  22. 22.x + 7y = 46 and 7x + y = 34 →
  23. 23.7x + 6y = 53 and 6x + 7y = 51 →
  24. 24.6x + 4y = −40 and 5x − 6y = 32 →
  25. 25.5x + 3y = 42 and 3x + y = 18 →
  26. 26.5x + 6y = 59 and 6x + 5y = 51 →
  27. 27.2x − 4y = 30 and 5x + y = 9 →
  28. 28.2x + 6y = 38 and x − y = −1 →
  29. 29.x + 4y = 27 and 4x − 4y = −72 →
  30. 30.2x + 7y = 75 and 7x + 2y = 60 →
  31. 31.3x + y = −8 and 6x + 5y = −13 →
  32. 32.4x + 3y = 42 and 2x + 6y = 30 →
  33. 33.3x + 8y = 27 and 8x + 3y = 17 →
  34. 34.5x − 4y = 37 and 4x + y = −4 →
  35. 35.5x + 9y = −58 and 9x + 5y = −26 →
  36. 36.8x + 4y = 80 and 4x + 8y = 52 →
  37. 37.7x + 3y = 10 and 3x + 7y = 50 →
  38. 38.2x − 6y = −58 and x + y = −1 →
  39. 39.3x + 5y = −3 and 5x + 3y = −21 →
  40. 40.x + 5y = 25 and 3x − 2y = 7 →

Answer key

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

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