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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 930 · 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. 1.3x + 4y = −42 and 5x + y = −19 →
  2. 2.9x + 7y = 53 and 7x + 9y = 59 →
  3. 3.5x + 3y = −1 and 3x + 5y = −23 →
  4. 4.x − y = −4 and 2x + y = −17 →
  5. 5.6x + 6y = 18 and 6x + y = 43 →
  6. 6.3x − 5y = 55 and 5x + y = 17 →
  7. 7.5x − 3y = 37 and 6x + 2y = 50 →
  8. 8.6x + 5y = −2 and 4x + y = −6 →
  9. 9.3x − y = −8 and 2x + 4y = −10 →
  10. 10.5x + 4y = 63 and 5x + 3y = 56 →
  11. 11.x + y = 8 and 2x − 6y = −56 →
  12. 12.6x + 5y = 69 and 4x − 2y = 30 →
  13. 13.7x + 8y = 67 and 8x + 7y = 68 →
  14. 14.6x + 4y = 42 and 2x + 6y = 56 →
  15. 15.8x + 5y = 32 and 5x + 8y = −19 →
  16. 16.4x + 6y = 58 and 4x + 2y = 22 →
  17. 17.5x + 4y = −27 and x − 5y = −17 →
  18. 18.8x + 7y = 17 and 7x + 8y = 13 →
  19. 19.3x + 2y = −5 and 2x + 3y = 0 →
  20. 20.5x − y = 16 and 5x + 4y = −14 →
  21. 21.4x − y = −9 and 4x + 3y = 11 →
  22. 22.5x + y = 18 and 6x − y = 4 →
  23. 23.6x + 3y = 60 and 4x − 6y = 24 →
  24. 24.3x + 2y = 34 and 3x − 4y = −14 →
  25. 25.2x + 8y = 76 and 8x + 2y = 64 →
  26. 26.x − 3y = −18 and x + 4y = 3 →
  27. 27.3x + 2y = 2 and 2x + 3y = −12 →
  28. 28.6x − 6y = −84 and 2x + 4y = 26 →
  29. 29.2x + y = −11 and x − 6y = −38 →
  30. 30.3x + y = 13 and x + 3y = −17 →
  31. 31.3x + 6y = 0 and 5x + 5y = −15 →
  32. 32.5x − 5y = 10 and 6x − 3y = 21 →
  33. 33.5x + 2y = 55 and 5x + 5y = 70 →
  34. 34.4x − 5y = −14 and 5x + 3y = 1 →
  35. 35.2x + 3y = −6 and 6x − 5y = −46 →
  36. 36.2x + 9y = −23 and 9x + 2y = 12 →
  37. 37.6x − y = 26 and 2x + 4y = 26 →
  38. 38.8x + 5y = −7 and 5x + 8y = −19 →
  39. 39.x − y = 2 and 2x + 2y = 12 →
  40. 40.5x + 4y = 29 and 4x + 5y = 25 →

Answer key

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

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