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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 67 · 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. 1.3x + y = 25 and x + 3y = 3 →
  2. 2.4x + 3y = −5 and 3x + 5y = 10 →
  3. 3.5x + 9y = 96 and 9x + 5y = 72 →
  4. 4.2x + 4y = 42 and 4x + 2y = 36 →
  5. 5.x + 9y = 58 and 9x + y = 42 →
  6. 6.3x + 5y = 53 and 5x − 2y = 16 →
  7. 7.6x + y = −20 and x + 6y = −15 →
  8. 8.3x + 2y = 28 and 2x + 3y = 22 →
  9. 9.2x − 4y = −46 and x + 6y = 33 →
  10. 10.2x + 6y = −18 and 5x + 2y = 33 →
  11. 11.6x − 2y = 28 and x + 5y = 10 →
  12. 12.4x + y = 34 and 4x + 4y = 40 →
  13. 13.3x + y = 19 and 6x + 3y = 39 →
  14. 14.2x + y = −4 and x + 5y = −29 →
  15. 15.5x + 9y = 98 and 9x + 5y = 98 →
  16. 16.2x + y = 3 and x + 3y = −21 →
  17. 17.2x + 3y = 15 and 3x + 2y = 0 →
  18. 18.4x + 6y = −66 and 6x + 4y = −54 →
  19. 19.3x + 8y = −3 and 8x + 3y = −63 →
  20. 20.x + 7y = 58 and 7x + y = 22 →
  21. 21.6x + 7y = 33 and 7x + 6y = 19 →
  22. 22.5x + 3y = −33 and 4x + 2y = −26 →
  23. 23.2x + 3y = 5 and 3x + 2y = 0 →
  24. 24.2x + 2y = −32 and 5x + 2y = −53 →
  25. 25.x + 9y = 70 and 9x + y = −10 →
  26. 26.2x − 4y = 42 and x + 4y = −21 →
  27. 27.7x + y = −1 and x + 7y = −55 →
  28. 28.3x − y = 1 and 5x + y = 23 →
  29. 29.7x + 3y = −44 and 3x + 7y = −36 →
  30. 30.4x + 5y = 23 and x + 3y = 4 →
  31. 31.4x + 4y = 16 and 2x + 3y = 14 →
  32. 32.6x + y = 12 and x − 5y = −29 →
  33. 33.6x + y = 24 and 5x − 2y = 3 →
  34. 34.x + y = 9 and 4x + 2y = 30 →
  35. 35.4x + 3y = −33 and 2x − y = −19 →
  36. 36.6x + 7y = −69 and 7x + 6y = −74 →
  37. 37.9x + 7y = 71 and 7x + 9y = 73 →
  38. 38.5x + y = 17 and 2x − y = 4 →
  39. 39.7x + 5y = −41 and 5x + 7y = −19 →
  40. 40.6x + 5y = 78 and 2x + 2y = 28 →

Answer key

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

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