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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 76 · 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 + y = 30 and 6x + 3y = 48 →
  2. 2.4x − 3y = 23 and 4x + 2y = −22 →
  3. 3.5x + 4y = 16 and 3x + 5y = 33 →
  4. 4.4x + y = −3 and x + 4y = 3 →
  5. 5.2x + 4y = 12 and 4x + 2y = 18 →
  6. 6.5x + 2y = 31 and 2x + 5y = −17 →
  7. 7.x + 5y = 20 and 5x + y = 28 →
  8. 8.x − 3y = −15 and 5x − 2y = 29 →
  9. 9.x − y = −2 and 6x + 6y = 36 →
  10. 10.6x + 5y = 2 and 5x + 6y = −2 →
  11. 11.x + 2y = 7 and 2x + y = −10 →
  12. 12.3x + 3y = −3 and 6x + 4y = 12 →
  13. 13.6x + 2y = −52 and 2x + 6y = −12 →
  14. 14.4x − 5y = −31 and 4x − 3y = −33 →
  15. 15.6x + y = −47 and 2x + y = −19 →
  16. 16.3x − 6y = −3 and x + 5y = 6 →
  17. 17.x + 4y = −31 and 4x + y = 11 →
  18. 18.5x − y = 18 and x + 3y = 26 →
  19. 19.x + y = 14 and 2x − 6y = −12 →
  20. 20.x − y = −1 and 3x + y = 9 →
  21. 21.3x + y = −9 and x + 3y = −19 →
  22. 22.3x + 2y = −2 and x + 2y = 2 →
  23. 23.9x + 5y = 73 and 5x + 9y = 53 →
  24. 24.8x + 6y = 20 and 6x + 8y = 36 →
  25. 25.x + 8y = 63 and 8x + y = 0 →
  26. 26.4x + 8y = 76 and 8x + 4y = 68 →
  27. 27.4x + 5y = 71 and 4x + 3y = 57 →
  28. 28.5x − y = 18 and 4x − 5y = 27 →
  29. 29.8x + y = 59 and x + 8y = 31 →
  30. 30.x + y = 6 and 3x − 4y = −17 →
  31. 31.4x + 4y = 40 and 3x + y = 28 →
  32. 32.x + 7y = 21 and 7x + y = 51 →
  33. 33.3x + y = 1 and x + 3y = 19 →
  34. 34.3x − 3y = −21 and 4x + y = −33 →
  35. 35.5x + 9y = −8 and 9x + 5y = −48 →
  36. 36.2x + 5y = 45 and x + 2y = 19 →
  37. 37.5x + 2y = −22 and 5x + 5y = −10 →
  38. 38.3x + 4y = −8 and 4x + 3y = 1 →
  39. 39.4x + 3y = 10 and 4x − 4y = 52 →
  40. 40.x + 6y = 26 and x + 4y = 20 →

Answer key

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

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