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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 476 · 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. 1.2x + 2y = 12 and 2x − y = 18 →
  2. 2.5x + 6y = −46 and 6x + 5y = −53 →
  3. 3.2x + y = 19 and 3x − 4y = 1 →
  4. 4.2x + y = −3 and x + 2y = 12 →
  5. 5.6x + 2y = 4 and 2x + 6y = −20 →
  6. 6.x + 2y = 2 and 6x − y = −14 →
  7. 7.x + 2y = −1 and x − 2y = −17 →
  8. 8.4x + 4y = 24 and 3x − 2y = 3 →
  9. 9.2x + 3y = −27 and x + 4y = −31 →
  10. 10.3x + 7y = 9 and 7x + 3y = −19 →
  11. 11.2x + 3y = 20 and 5x + 4y = 29 →
  12. 12.2x − 3y = −25 and x + 5y = 46 →
  13. 13.4x + 4y = −24 and 4x − 4y = −16 →
  14. 14.4x + 5y = 16 and 6x − 4y = 70 →
  15. 15.4x − 3y = 0 and 3x − y = 5 →
  16. 16.5x + 6y = −28 and 5x − 3y = 44 →
  17. 17.2x + 2y = −22 and x + 3y = −17 →
  18. 18.6x + y = 38 and x + 6y = 53 →
  19. 19.8x + y = −46 and x + 8y = 10 →
  20. 20.7x + 2y = −44 and 2x + 7y = 26 →
  21. 21.2x + y = −1 and 3x − 2y = −26 →
  22. 22.7x + 2y = −47 and 2x + 7y = 38 →
  23. 23.7x + 6y = −84 and 6x + 7y = −85 →
  24. 24.5x + 5y = 30 and x + 5y = −6 →
  25. 25.5x + 7y = 84 and 7x + 5y = 84 →
  26. 26.x − y = −4 and x − 2y = −1 →
  27. 27.x − 2y = −12 and x + y = 15 →
  28. 28.6x − 3y = 12 and 2x + 2y = 10 →
  29. 29.5x + 6y = −22 and 6x + 5y = −11 →
  30. 30.2x + 5y = −7 and 3x + 6y = −9 →
  31. 31.2x + 4y = 34 and 4x + y = 26 →
  32. 32.x − 3y = −7 and x − 5y = −9 →
  33. 33.2x + y = 4 and 3x + 5y = 34 →
  34. 34.3x − 6y = −57 and x + 5y = 16 →
  35. 35.3x + 5y = −31 and 6x + 2y = 2 →
  36. 36.8x + 7y = −50 and 7x + 8y = −55 →
  37. 37.6x + y = 35 and x + 6y = 0 →
  38. 38.9x + 8y = 35 and 8x + 9y = 33 →
  39. 39.3x + 9y = −33 and 9x + 3y = −3 →
  40. 40.4x − 4y = 12 and 5x + 5y = 55 →

Answer key

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

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