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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 291 · 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 x − 4y = 0 →
  2. 2.4x + 3y = −12 and 4x + 2y = −20 →
  3. 3.3x + 2y = −24 and x + 6y = −56 →
  4. 4.7x + y = 6 and x + 7y = −6 →
  5. 5.6x + 3y = 6 and 2x − 2y = 26 →
  6. 6.6x + 3y = −60 and 2x + 4y = −32 →
  7. 7.2x + 6y = 44 and 6x + 2y = −12 →
  8. 8.2x − 5y = −4 and 2x + 2y = 24 →
  9. 9.3x + 5y = −28 and 3x + y = −20 →
  10. 10.2x + 2y = −2 and 2x + 4y = 8 →
  11. 11.6x + 2y = 24 and 4x + 6y = 58 →
  12. 12.4x + 3y = −56 and 3x + 4y = −56 →
  13. 13.4x − 5y = −49 and 6x + 3y = −21 →
  14. 14.2x − 5y = 35 and x − y = 10 →
  15. 15.2x − 6y = 28 and 5x + y = 6 →
  16. 16.3x + 4y = 13 and x + 2y = 3 →
  17. 17.6x + 4y = 22 and 2x + y = 7 →
  18. 18.4x + y = −10 and 4x + 6y = 20 →
  19. 19.6x + 7y = 45 and 7x + 6y = 46 →
  20. 20.5x + 3y = 52 and x − y = 4 →
  21. 21.2x + 6y = 72 and 3x + 4y = 63 →
  22. 22.3x + 3y = −9 and 5x + 3y = −5 →
  23. 23.3x + 6y = 6 and 4x − 2y = −32 →
  24. 24.x − 6y = −39 and 6x + 3y = 78 →
  25. 25.9x + 8y = 57 and 8x + 9y = 62 →
  26. 26.2x + 3y = 15 and 4x + 5y = 27 →
  27. 27.4x + 5y = 68 and 5x + 4y = 67 →
  28. 28.3x + 9y = −3 and 9x + 3y = −33 →
  29. 29.3x + 3y = 51 and 2x + 5y = 58 →
  30. 30.4x + 9y = 29 and 9x + 4y = −16 →
  31. 31.2x − 5y = 11 and 4x + y = −11 →
  32. 32.4x + 6y = −34 and 6x + 3y = −21 →
  33. 33.x + 4y = 19 and 2x − 6y = −4 →
  34. 34.x + 3y = 5 and 6x − y = 11 →
  35. 35.4x − 3y = −60 and 3x + y = −19 →
  36. 36.5x − 3y = 14 and 3x − 2y = 7 →
  37. 37.7x + 2y = 23 and 2x + 7y = 58 →
  38. 38.4x − 4y = −40 and 2x + 4y = 4 →
  39. 39.3x + y = 22 and 4x + 2y = 32 →
  40. 40.3x + 5y = 63 and 5x + 3y = 57 →

Answer key

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

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