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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 559 · 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 + 2y = −14 and 2x + 7y = 41 →
  2. 2.3x + 5y = −39 and 5x + 3y = −17 →
  3. 3.2x − y = 8 and 4x + 3y = 26 →
  4. 4.6x + y = 19 and x + 6y = 9 →
  5. 5.4x + 5y = 69 and 5x − y = 21 →
  6. 6.7x + 6y = −40 and 6x + 7y = −51 →
  7. 7.2x + 6y = −20 and 6x + 4y = −32 →
  8. 8.4x + 2y = 2 and 5x + 6y = −8 →
  9. 9.4x − 6y = 16 and x + y = −11 →
  10. 10.x + 9y = 23 and 9x + y = 47 →
  11. 11.2x + 3y = 12 and 3x + 2y = 13 →
  12. 12.4x + 7y = −18 and 7x + 4y = −48 →
  13. 13.3x + y = −7 and 4x − 3y = −18 →
  14. 14.2x + 6y = 42 and 6x + y = −27 →
  15. 15.x + 6y = 27 and 6x + y = 22 →
  16. 16.4x + 5y = 37 and 5x + 5y = 45 →
  17. 17.4x + y = −27 and 2x − 3y = −17 →
  18. 18.6x − 4y = 44 and 3x + y = −2 →
  19. 19.4x + 5y = 63 and x + y = 14 →
  20. 20.9x + 2y = 34 and 2x + 9y = −1 →
  21. 21.2x + y = 12 and 5x − y = 9 →
  22. 22.x + 4y = 2 and x + 6y = 4 →
  23. 23.6x + 2y = 28 and 2x + 6y = 20 →
  24. 24.6x − y = 30 and 4x + 5y = −14 →
  25. 25.9x + 7y = −108 and 7x + 9y = −116 →
  26. 26.6x + 2y = −10 and 2x + 6y = −46 →
  27. 27.2x + 9y = 39 and 9x + 2y = 60 →
  28. 28.4x − 2y = 22 and 3x + 2y = 41 →
  29. 29.3x + 8y = −32 and 8x + 3y = −67 →
  30. 30.2x + 5y = 43 and 3x − y = 22 →
  31. 31.4x + 6y = 20 and 5x + 4y = 4 →
  32. 32.2x + y = 21 and x + 2y = 24 →
  33. 33.8x + 5y = −12 and 5x + 8y = −27 →
  34. 34.x + 4y = 41 and 4x + y = 29 →
  35. 35.4x + 3y = 43 and 6x + 6y = 72 →
  36. 36.3x − y = −12 and x − 4y = 29 →
  37. 37.6x + 3y = 57 and 2x + 2y = 20 →
  38. 38.x + 3y = −15 and 3x + 3y = −9 →
  39. 39.7x + 8y = 15 and 8x + 7y = 0 →
  40. 40.5x + 3y = 33 and 4x + 6y = 30 →

Answer key

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

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