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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 18 · 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 + 6y = −18 and 3x − y = −5 →
  2. 2.6x + 4y = 64 and 4x + 6y = 66 →
  3. 3.x − 2y = −9 and 5x + 5y = 90 →
  4. 4.2x + 3y = −11 and 4x + 2y = 14 →
  5. 5.2x + 8y = −6 and 8x + 2y = 66 →
  6. 6.x + 9y = 19 and 9x + y = 11 →
  7. 7.3x + 6y = 42 and 6x + 5y = 56 →
  8. 8.6x + 5y = −8 and 6x + 4y = −10 →
  9. 9.x − 3y = 5 and 2x − 2y = 2 →
  10. 10.5x + 3y = 31 and x − 3y = −1 →
  11. 11.2x + 4y = 10 and 4x − y = −43 →
  12. 12.2x + y = 14 and x − y = 4 →
  13. 13.5x + y = 18 and x + 5y = 42 →
  14. 14.2x + 9y = 35 and 9x + 2y = 42 →
  15. 15.6x − 3y = −48 and 2x + 2y = 8 →
  16. 16.9x + 4y = 55 and 4x + 9y = 75 →
  17. 17.2x + 2y = 0 and 5x − 4y = −63 →
  18. 18.7x + 3y = 57 and 3x + 7y = 13 →
  19. 19.x + 4y = 26 and 2x + y = 17 →
  20. 20.3x + 6y = 6 and 6x + 3y = 39 →
  21. 21.5x + 6y = −65 and 6x + 5y = −67 →
  22. 22.4x − 4y = 4 and 4x + 6y = −56 →
  23. 23.x + y = −3 and 4x − y = 23 →
  24. 24.4x + 3y = 25 and 3x + 2y = 19 →
  25. 25.7x + 9y = 30 and 9x + 7y = 34 →
  26. 26.5x + 4y = −14 and x − 6y = −30 →
  27. 27.4x + 4y = 16 and 6x − 3y = −30 →
  28. 28.4x − 4y = −28 and 6x − 5y = −38 →
  29. 29.x + 3y = 13 and 3x + y = 7 →
  30. 30.9x + 4y = −25 and 4x + 9y = −40 →
  31. 31.5x + 2y = −21 and 2x + 5y = 0 →
  32. 32.2x + 5y = 22 and x + 2y = 9 →
  33. 33.3x + y = 11 and 2x − y = −6 →
  34. 34.2x + 5y = 42 and x − 6y = −30 →
  35. 35.4x + 2y = 6 and 2x + 6y = 8 →
  36. 36.5x + 4y = 15 and 2x − 2y = −12 →
  37. 37.6x + y = 10 and 6x + 4y = 22 →
  38. 38.3x − 6y = −18 and 6x − 4y = 12 →
  39. 39.6x + 2y = 12 and x + 5y = −26 →
  40. 40.2x + 3y = 8 and x − 5y = −9 →

Answer key

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

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