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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 747 · 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 = 22 and 3x + 2y = 17 →
  2. 2.x + 2y = 0 and 6x − 4y = 16 →
  3. 3.x + 8y = 31 and 8x + y = −67 →
  4. 4.2x + y = −13 and x + 2y = −17 →
  5. 5.2x + 6y = −36 and 6x − 2y = 32 →
  6. 6.3x − 5y = −17 and 6x − 6y = −18 →
  7. 7.2x + 7y = 46 and 7x + 2y = −19 →
  8. 8.x − y = 0 and x + 3y = 16 →
  9. 9.x − y = −1 and 4x − 6y = 6 →
  10. 10.7x + 4y = 52 and 4x + 7y = 58 →
  11. 11.4x + 2y = 22 and x − 4y = 1 →
  12. 12.4x + 6y = 38 and 4x + 2y = 2 →
  13. 13.6x + 6y = 66 and 4x + 6y = 62 →
  14. 14.3x + y = −19 and x + 3y = −1 →
  15. 15.2x + 4y = −20 and x + 5y = −34 →
  16. 16.5x + 2y = 42 and 2x + y = 18 →
  17. 17.6x − y = −7 and x + y = 0 →
  18. 18.9x + 2y = −37 and 2x + 9y = 26 →
  19. 19.3x + y = 6 and x + 4y = 13 →
  20. 20.2x + y = −2 and x + 2y = −10 →
  21. 21.2x − 2y = 6 and 3x + 6y = 36 →
  22. 22.6x + 4y = 50 and 4x + 6y = 40 →
  23. 23.4x + y = −21 and 3x − y = −21 →
  24. 24.5x + 2y = −31 and x + 4y = 19 →
  25. 25.4x + y = 12 and x + 4y = −27 →
  26. 26.7x + 8y = 7 and 8x + 7y = −7 →
  27. 27.x + 9y = 79 and 9x + y = −9 →
  28. 28.6x + 5y = −3 and x + 2y = 10 →
  29. 29.8x + 6y = −20 and 6x + 8y = −8 →
  30. 30.3x + 6y = −69 and 4x − 2y = −22 →
  31. 31.5x + 3y = −47 and 3x + 5y = −57 →
  32. 32.5x + 4y = −31 and 6x + 6y = −48 →
  33. 33.5x + 7y = 44 and 7x + 5y = 52 →
  34. 34.3x + 4y = −12 and 5x + 5y = −5 →
  35. 35.9x + y = 47 and x + 9y = 23 →
  36. 36.6x + 3y = 63 and x − 6y = −22 →
  37. 37.2x + 4y = −20 and 6x + 6y = −12 →
  38. 38.3x + y = −15 and x + 3y = −21 →
  39. 39.5x − 6y = −57 and x + 5y = 1 →
  40. 40.9x + 2y = 73 and 2x + 9y = −18 →

Answer key

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

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