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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 147 · 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. 1.5x + 4y = −15 and 4x + 5y = −3 →
  2. 2.5x + 3y = 58 and 3x + 5y = 54 →
  3. 3.4x + 7y = −23 and 7x + 4y = 1 →
  4. 4.3x + y = −10 and 6x + 5y = −14 →
  5. 5.3x + y = 10 and x + 3y = 22 →
  6. 6.4x + 6y = 40 and 3x + 4y = 27 →
  7. 7.x + 8y = 2 and 8x + y = −47 →
  8. 8.5x + y = 48 and 3x − y = 24 →
  9. 9.4x + y = 7 and 2x + 4y = −28 →
  10. 10.x + 7y = 26 and 7x + y = −10 →
  11. 11.3x − 5y = 31 and 2x − 4y = 26 →
  12. 12.2x + 4y = 18 and 4x + y = 29 →
  13. 13.5x − 6y = −59 and x + 4y = 9 →
  14. 14.2x + 6y = 14 and 2x − 6y = −10 →
  15. 15.x + 3y = 22 and 4x + 5y = 53 →
  16. 16.2x + 2y = 16 and 2x − 4y = 10 →
  17. 17.5x − 5y = 10 and 3x + 6y = 15 →
  18. 18.3x − 3y = −21 and x − 2y = −15 →
  19. 19.4x + y = 43 and 3x + 3y = 48 →
  20. 20.2x − 4y = −18 and 6x + 4y = −38 →
  21. 21.x + 4y = −9 and x + 5y = −12 →
  22. 22.x + 3y = −25 and 5x + 6y = −44 →
  23. 23.6x + y = 50 and 6x + 4y = 38 →
  24. 24.7x + y = −37 and x + 7y = 29 →
  25. 25.6x + 3y = 6 and 2x + 4y = 14 →
  26. 26.3x + 4y = 6 and 4x + 3y = 1 →
  27. 27.9x + 2y = −11 and 2x + 9y = 66 →
  28. 28.x + 9y = −65 and 9x + y = 55 →
  29. 29.9x + 2y = −73 and 2x + 9y = 18 →
  30. 30.3x − 6y = −51 and 2x − 5y = −43 →
  31. 31.x + 4y = 5 and 5x + 3y = 42 →
  32. 32.3x + 6y = 18 and x + 3y = 5 →
  33. 33.3x − 6y = −39 and 3x + 6y = 33 →
  34. 34.x + y = −4 and 4x + 3y = −17 →
  35. 35.2x + y = 15 and x + 2y = 21 →
  36. 36.8x + y = 71 and x + 8y = 1 →
  37. 37.4x + 9y = 49 and 9x + 4y = 29 →
  38. 38.5x + 9y = −29 and 9x + 5y = 15 →
  39. 39.7x + y = 10 and x + 7y = 22 →
  40. 40.4x + 2y = 36 and 6x − 6y = 18 →

Answer key

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

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