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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 784 · 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.x + 5y = 2 and 2x + 2y = −12 →
  2. 2.6x + 4y = −28 and 6x + 6y = −18 →
  3. 3.6x + 3y = 12 and 3x − 4y = −27 →
  4. 4.3x + 4y = 31 and 2x + y = 9 →
  5. 5.4x − 4y = −40 and x − 4y = −31 →
  6. 6.4x + 2y = 20 and 5x − 4y = −27 →
  7. 7.x + 8y = 17 and 8x + y = −53 →
  8. 8.x − y = −8 and 5x + 2y = 23 →
  9. 9.2x + 5y = −6 and 2x − 4y = 12 →
  10. 10.4x + 4y = 16 and x + 3y = 8 →
  11. 11.4x − 4y = 32 and 5x + 6y = −26 →
  12. 12.x + 2y = 20 and 2x + 5y = 48 →
  13. 13.3x + 6y = −72 and 3x + 2y = −36 →
  14. 14.2x + y = 10 and x + 2y = 14 →
  15. 15.3x − 4y = 23 and 2x + 4y = −18 →
  16. 16.4x − 4y = −20 and 2x + 5y = 46 →
  17. 17.6x + 3y = 18 and 2x − 2y = −6 →
  18. 18.9x + y = 38 and x + 9y = 22 →
  19. 19.3x + 9y = −9 and 9x + 3y = −75 →
  20. 20.3x + 4y = 43 and 4x + 3y = 48 →
  21. 21.x + 2y = 19 and 2x + 2y = 26 →
  22. 22.x + 2y = 10 and 2x + y = −1 →
  23. 23.3x + 8y = 22 and 8x + 3y = 22 →
  24. 24.5x + 2y = −24 and x − 3y = −32 →
  25. 25.6x − 3y = −24 and 5x + 4y = −33 →
  26. 26.8x + 5y = 27 and 5x + 8y = 51 →
  27. 27.6x + y = 32 and 6x − 6y = 60 →
  28. 28.2x + 9y = 45 and 9x + 2y = −67 →
  29. 29.3x + 3y = 18 and 2x − 5y = 33 →
  30. 30.3x + 6y = 27 and 4x + 2y = 12 →
  31. 31.x + y = −1 and 6x + 5y = −8 →
  32. 32.6x + 3y = −39 and 2x + 3y = −3 →
  33. 33.3x + 6y = 27 and 4x + 6y = 24 →
  34. 34.5x + 6y = 31 and x − 6y = −1 →
  35. 35.2x − y = −13 and 3x + y = −17 →
  36. 36.5x + 2y = −32 and 2x + 5y = −17 →
  37. 37.4x + 5y = 51 and 5x + 4y = 57 →
  38. 38.4x + 4y = 20 and 3x + 6y = 18 →
  39. 39.x + 4y = 38 and 4x + y = 17 →
  40. 40.4x + 8y = −12 and 8x + 4y = −48 →

Answer key

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

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