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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 98 · 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. 1.5x − 5y = 5 and 4x + y = 19 →
  2. 2.2x + 5y = −63 and 6x + 3y = −81 →
  3. 3.5x + 5y = 25 and x − 5y = −19 →
  4. 4.4x + 9y = −11 and 9x + 4y = −41 →
  5. 5.9x + 3y = −27 and 3x + 9y = 15 →
  6. 6.6x − 5y = 1 and x + 3y = 4 →
  7. 7.6x + y = 63 and x + 2y = 27 →
  8. 8.4x + y = −30 and 3x − 4y = −51 →
  9. 9.3x + 2y = 21 and 6x − 6y = 12 →
  10. 10.6x − 4y = −4 and 3x − 6y = −30 →
  11. 11.2x − y = −3 and 4x + 3y = 19 →
  12. 12.4x + 6y = −10 and x − 2y = 8 →
  13. 13.2x + 2y = 10 and 6x − 4y = 40 →
  14. 14.4x + 2y = 6 and 3x + 6y = 27 →
  15. 15.6x − y = 30 and 3x + y = 6 →
  16. 16.9x + 8y = 129 and 8x + 9y = 126 →
  17. 17.2x − 2y = −4 and 3x − 5y = 2 →
  18. 18.4x + 7y = 13 and 7x + 4y = −2 →
  19. 19.x + 5y = 28 and 3x + y = 0 →
  20. 20.9x + y = 87 and x + 9y = 63 →
  21. 21.x + 4y = 3 and 6x + y = −28 →
  22. 22.5x − 3y = 20 and 2x + 2y = 24 →
  23. 23.x + y = −9 and 2x + 3y = −26 →
  24. 24.x + 5y = −46 and 2x + 5y = −52 →
  25. 25.2x + 8y = 58 and 8x + 2y = 52 →
  26. 26.4x + 7y = 39 and 7x + 4y = 60 →
  27. 27.3x − 5y = 18 and x + 4y = −11 →
  28. 28.2x + 9y = −9 and 9x + 2y = −79 →
  29. 29.2x + y = 18 and 2x − 5y = −18 →
  30. 30.4x + y = 39 and 4x − 5y = 21 →
  31. 31.6x + 5y = −16 and 5x + 6y = −6 →
  32. 32.x + 9y = 74 and 9x + y = 26 →
  33. 33.3x + 4y = −1 and 2x + 2y = 4 →
  34. 34.x − 2y = −7 and 4x + y = −1 →
  35. 35.x − y = −3 and 2x + 5y = 1 →
  36. 36.x − 2y = 8 and x + 2y = 0 →
  37. 37.5x + 3y = 11 and 5x + 4y = 3 →
  38. 38.x + 2y = 14 and 5x + 4y = 52 →
  39. 39.2x + 3y = 21 and 3x + 4y = 29 →
  40. 40.6x + 3y = 12 and 6x − y = −20 →

Answer key

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

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