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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 637 · 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 = −14 and 6x − 5y = −13 →
  2. 2.x + 2y = 6 and x − y = 0 →
  3. 3.2x − 3y = 15 and 3x − y = 26 →
  4. 4.2x + 8y = 56 and 8x + 2y = −46 →
  5. 5.x − 2y = −21 and 4x + 3y = 4 →
  6. 6.x + 6y = 27 and 4x + 2y = 20 →
  7. 7.2x + 2y = 4 and x + 3y = −8 →
  8. 8.8x + 3y = 1 and 3x + 8y = −34 →
  9. 9.2x + y = −24 and x + y = −16 →
  10. 10.6x + 3y = 15 and 5x − 6y = 4 →
  11. 11.2x + 6y = −62 and 6x + 2y = −58 →
  12. 12.2x − y = −17 and 2x + 2y = −8 →
  13. 13.x + 2y = −8 and 2x + 3y = −11 →
  14. 14.x + 6y = −41 and 6x + 2y = −42 →
  15. 15.6x − y = 22 and x − 5y = 23 →
  16. 16.4x + 7y = 42 and 7x + 4y = 57 →
  17. 17.2x + 3y = −37 and 6x + 4y = −66 →
  18. 18.5x + y = 10 and x + 5y = −22 →
  19. 19.3x + 5y = 6 and x + 5y = 12 →
  20. 20.6x + 5y = 63 and 3x − 6y = 6 →
  21. 21.6x + 5y = 84 and 2x + 5y = 48 →
  22. 22.6x − 2y = 72 and 2x + 4y = −18 →
  23. 23.2x + 4y = −12 and 6x + 5y = −43 →
  24. 24.6x + 2y = 28 and 4x + 2y = 20 →
  25. 25.6x − 2y = −40 and 6x + 2y = −20 →
  26. 26.3x − 4y = −33 and x − y = −8 →
  27. 27.6x + y = −39 and x + y = −9 →
  28. 28.2x + 6y = −20 and 3x + y = 2 →
  29. 29.3x − 5y = 1 and 5x + 6y = 59 →
  30. 30.2x + 6y = 40 and 3x + 4y = 20 →
  31. 31.x − 2y = −21 and 4x + 6y = 0 →
  32. 32.5x + 2y = 29 and 4x + y = 19 →
  33. 33.x + 4y = −3 and x − y = 2 →
  34. 34.6x + 4y = −44 and x + 5y = −42 →
  35. 35.8x + 2y = 88 and 2x + 8y = 82 →
  36. 36.x + 2y = −7 and 2x + y = −2 →
  37. 37.x + 8y = 12 and 8x + y = 33 →
  38. 38.3x − 4y = −25 and 2x − 6y = −20 →
  39. 39.x + 2y = −14 and 2x + 3y = −24 →
  40. 40.5x + 4y = 61 and 4x + 5y = 65 →

Answer key

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

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