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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 137 · 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. 1.7x + 4y = 28 and 4x + 7y = −17 →
  2. 2.4x − 2y = 16 and 6x − 5y = 28 →
  3. 3.4x + 8y = −4 and 8x + 4y = −20 →
  4. 4.3x + 3y = 18 and 5x + 2y = 18 →
  5. 5.3x + 9y = 42 and 9x + 3y = 30 →
  6. 6.2x + 9y = 78 and 9x + 2y = 43 →
  7. 7.2x + 6y = −10 and 6x + 4y = 12 →
  8. 8.3x + 2y = 19 and 2x + 3y = 16 →
  9. 9.9x + 7y = 126 and 7x + 9y = 130 →
  10. 10.8x + 7y = 29 and 7x + 8y = 31 →
  11. 11.6x − 6y = 36 and 2x − y = 13 →
  12. 12.5x + 8y = 21 and 8x + 5y = −21 →
  13. 13.2x + 3y = 9 and 3x + 2y = 1 →
  14. 14.6x + 9y = −3 and 9x + 6y = −12 →
  15. 15.4x − 6y = 62 and 6x + y = 3 →
  16. 16.5x − 2y = 17 and 5x + 4y = 41 →
  17. 17.3x − 5y = −53 and 6x + y = −29 →
  18. 18.3x + 8y = 37 and 8x + 3y = −48 →
  19. 19.6x + 7y = 73 and 7x + 6y = 70 →
  20. 20.7x + 8y = 9 and 8x + 7y = 6 →
  21. 21.9x + 3y = 102 and 3x + 9y = 90 →
  22. 22.3x + 3y = 30 and 5x + y = 26 →
  23. 23.4x + y = −9 and x + y = −3 →
  24. 24.3x + 5y = 69 and x + 5y = 53 →
  25. 25.2x − 6y = −30 and 2x + 2y = −6 →
  26. 26.6x − 2y = −30 and 4x + 4y = −4 →
  27. 27.4x + 4y = −12 and x − 2y = 0 →
  28. 28.x + 7y = 0 and 7x + y = −48 →
  29. 29.7x + 5y = −2 and 5x + 7y = 26 →
  30. 30.x + 5y = 7 and x − y = −5 →
  31. 31.x − y = 5 and 6x − y = 40 →
  32. 32.6x + y = 41 and x + 6y = −34 →
  33. 33.2x − y = 10 and 4x − 3y = 22 →
  34. 34.9x + 4y = −49 and 4x + 9y = 36 →
  35. 35.x + y = 7 and 2x + 3y = 22 →
  36. 36.3x − 5y = 14 and 3x + 5y = 34 →
  37. 37.6x − 2y = 4 and 3x + 6y = 9 →
  38. 38.6x − 3y = 30 and 3x − y = 17 →
  39. 39.7x + 9y = −40 and 9x + 7y = −56 →
  40. 40.6x + 5y = −29 and x + 3y = 6 →

Answer key

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

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