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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 170 · 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 + 2y = −46 and 3x − 5y = 11 →
  2. 2.4x + 4y = −12 and x + 6y = 12 →
  3. 3.3x + 2y = 30 and 2x + 3y = 35 →
  4. 4.7x + 8y = 128 and 8x + 7y = 127 →
  5. 5.3x + 4y = −8 and 4x + 3y = −20 →
  6. 6.5x + 9y = −51 and 9x + 5y = −47 →
  7. 7.6x + 2y = 18 and 6x − 3y = 3 →
  8. 8.2x + 8y = −40 and 8x + 2y = 50 →
  9. 9.2x − 2y = 14 and 3x + 4y = −14 →
  10. 10.5x − 4y = 3 and x + 3y = 31 →
  11. 11.x + 4y = 42 and x + 2y = 24 →
  12. 12.6x + 4y = −38 and 2x + 5y = 2 →
  13. 13.2x + 3y = 34 and 2x + 2y = 26 →
  14. 14.3x + y = 24 and 6x + 5y = 57 →
  15. 15.4x − 2y = −48 and 4x + 4y = −12 →
  16. 16.5x + 4y = 43 and 2x + y = 13 →
  17. 17.2x + y = 9 and x − 2y = −3 →
  18. 18.9x + 5y = −42 and 5x + 9y = −42 →
  19. 19.8x + 7y = 73 and 7x + 8y = 77 →
  20. 20.2x + 2y = −2 and 3x − 5y = −43 →
  21. 21.x − y = 6 and 6x − 2y = 44 →
  22. 22.5x + 3y = 1 and 3x + 5y = −25 →
  23. 23.2x + 2y = −4 and 2x + 3y = −13 →
  24. 24.5x + 7y = −18 and 7x + 5y = 18 →
  25. 25.9x + 3y = 66 and 3x + 9y = 6 →
  26. 26.4x − 2y = −2 and 6x + 3y = 39 →
  27. 27.x − 2y = −14 and x − 4y = −32 →
  28. 28.2x + y = 11 and x + 2y = 4 →
  29. 29.6x − 5y = 1 and 2x + 2y = 4 →
  30. 30.4x + 6y = 42 and x − 2y = −21 →
  31. 31.5x + 2y = 0 and x + 3y = −13 →
  32. 32.5x + 6y = 17 and 4x + 6y = 16 →
  33. 33.5x − y = −43 and x + y = −5 →
  34. 34.6x + 9y = 93 and 9x + 6y = 72 →
  35. 35.4x − 5y = 29 and x − y = 6 →
  36. 36.8x + 5y = −44 and 5x + 8y = −8 →
  37. 37.6x − 2y = 26 and 6x − y = 31 →
  38. 38.3x − 6y = 33 and 4x + 2y = −26 →
  39. 39.x + 3y = 13 and 3x + y = 15 →
  40. 40.6x − 2y = −62 and 3x + 5y = −7 →

Answer key

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

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