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????????????????????? 1 ?????????? 2555 ?.3 ???????

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1. This document contains 30 systems of linear equations with their corresponding solutions. 2. The linear systems range from 2 to 4 equations each and are presented in a table format with the equations on the left and solutions on the right. 3. The solutions include points such as (0,3), (-2,0), and (-1,4) as well as lists of points like (1,4), (7,7), (-3,-8).

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1 1 2555 23101 3 30 60 1. 48 64 384 512 2. 108 187 216 432 3. 4. 308 341 748 836 5. 1 8
2 11,088 21,088 6. 7. 36 20 3 100 120 160 180 8. 10 21 421.48 419.86 417.84 413.16 9. 8 550 570 600 610 10. 2y + 5x = 10
3 11. y = 1 x + 3 , y = 2x + 3 2 y = 3x ¨C 5 , y = 3x + 5 x = ¨C3 , y = 6 y = 3x , y = 1 12. (3, ¨C2) x ¨C 4y = 6 y + 4x ¨C 10 = 0 x ¨C 4y + 14 = 0 4y ¨C x + 11 = 0 y + 4x + 5 = 0 13. 2x + 3y = 7 , 4x + 6y = 11 8x ¨C 12 = 3 , 3x + 2y = 2
4 5x ¨C 2y = 7 , 2x + 5y = 11 y ¨C 2 x = ¨C5 , 2y ¨C 3 3x = 1 14. (2, 1), (8,-1), (-5, -3) (1, 3), (0, 2), (-1, 1) (6, 1), (-4, 3), (0, 2) (-1, 1), (-5, 1), (-3, -8) 15. 7x ¨C y = 3 (1, 4) (-1, 4) (1, -4) (-1, -4) 16. (3, -5) x - 6y + 1 = 0 x + 3y - 12 = 0 2x ¨C y ¨C 11 = 0 2 x ¨C 3y + 1 = 0 17. (1, 0), (3, 6), (-1, -2) (-1, 0), (3, -6), (-3, -5) (1, 0), (-1, -2), (0, -1) (-1, 0), (0, -2), (-2, -6) 18. x (6, 6), (7, 7), (-3, -8) (1, 4), (7, 7), (-3, -8) (1, 4), (7, 7), (-3, -8)
5 (1, 4), (7, 7), (-3, -8) 19. 5x + 2y = 0 (0, 0) (2, -5) (-2, -5) (-2, 5) 20. 0, 0) 2x ¨C y = 0 7x - y + 1 = 0 5x + 2y = 3 y¨Cx=5 21. 2, -1) 5x ¨C 2y + 1 = 0 5x ¨C 2y = 0 2x ¨C y - 5 = -0 2x ¨C y = -0 22. 3x + y = 1 1, -2) 2x + y = 4 5x ¨C y = 7 2x - y = 4 5x + y = -7 23. 2x + 1 = 0 7y ¨C 9 = 0 2x (y ¨C 4) = 5
6 2x ¨C 3y = -0 24. (0, 2) x¨Cy=0 7x ¨C 3y = -5 9x ¨C y + 2 = 0 5x + y = 6 25. y = 2x + 1 4x ¨C y + 1 = 0 2x + y + 3 = 0 2x ¨C y ¨C 9 = 0 4x + y - 5 = 0 26. x 2x ¨C 3 = 7 5 ¨C 7y = 2 2x + 7y = 1 5y ¨C x = -8 27. y 2y + 1 = 0 7x ¨C 4 = 6 5x - 7y = 3 y ¨C 3x = -4 28. 2x ¨C y = 6 X
7 (0, 3) (3, 0) (-3, 0) (0, -3) 29.6x ¨C 5y =10 Y (-2, 0) (2, 0) (0, 2) (0, -2) 30. 2x ¨C y = 6 x + 2y + 2 = 0 (-2, 2) (3, -1) (1, -3) (2, -2) 4 !

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????????????????????? 1 ?????????? 2555 ?.3 ???????

  • 1. 1 1 2555 23101 3 30 60 1. 48 64 384 512 2. 108 187 216 432 3. 4. 308 341 748 836 5. 1 8
  • 2. 2 11,088 21,088 6. 7. 36 20 3 100 120 160 180 8. 10 21 421.48 419.86 417.84 413.16 9. 8 550 570 600 610 10. 2y + 5x = 10
  • 3. 3 11. y = 1 x + 3 , y = 2x + 3 2 y = 3x ¨C 5 , y = 3x + 5 x = ¨C3 , y = 6 y = 3x , y = 1 12. (3, ¨C2) x ¨C 4y = 6 y + 4x ¨C 10 = 0 x ¨C 4y + 14 = 0 4y ¨C x + 11 = 0 y + 4x + 5 = 0 13. 2x + 3y = 7 , 4x + 6y = 11 8x ¨C 12 = 3 , 3x + 2y = 2
  • 4. 4 5x ¨C 2y = 7 , 2x + 5y = 11 y ¨C 2 x = ¨C5 , 2y ¨C 3 3x = 1 14. (2, 1), (8,-1), (-5, -3) (1, 3), (0, 2), (-1, 1) (6, 1), (-4, 3), (0, 2) (-1, 1), (-5, 1), (-3, -8) 15. 7x ¨C y = 3 (1, 4) (-1, 4) (1, -4) (-1, -4) 16. (3, -5) x - 6y + 1 = 0 x + 3y - 12 = 0 2x ¨C y ¨C 11 = 0 2 x ¨C 3y + 1 = 0 17. (1, 0), (3, 6), (-1, -2) (-1, 0), (3, -6), (-3, -5) (1, 0), (-1, -2), (0, -1) (-1, 0), (0, -2), (-2, -6) 18. x (6, 6), (7, 7), (-3, -8) (1, 4), (7, 7), (-3, -8) (1, 4), (7, 7), (-3, -8)
  • 5. 5 (1, 4), (7, 7), (-3, -8) 19. 5x + 2y = 0 (0, 0) (2, -5) (-2, -5) (-2, 5) 20. 0, 0) 2x ¨C y = 0 7x - y + 1 = 0 5x + 2y = 3 y¨Cx=5 21. 2, -1) 5x ¨C 2y + 1 = 0 5x ¨C 2y = 0 2x ¨C y - 5 = -0 2x ¨C y = -0 22. 3x + y = 1 1, -2) 2x + y = 4 5x ¨C y = 7 2x - y = 4 5x + y = -7 23. 2x + 1 = 0 7y ¨C 9 = 0 2x (y ¨C 4) = 5
  • 6. 6 2x ¨C 3y = -0 24. (0, 2) x¨Cy=0 7x ¨C 3y = -5 9x ¨C y + 2 = 0 5x + y = 6 25. y = 2x + 1 4x ¨C y + 1 = 0 2x + y + 3 = 0 2x ¨C y ¨C 9 = 0 4x + y - 5 = 0 26. x 2x ¨C 3 = 7 5 ¨C 7y = 2 2x + 7y = 1 5y ¨C x = -8 27. y 2y + 1 = 0 7x ¨C 4 = 6 5x - 7y = 3 y ¨C 3x = -4 28. 2x ¨C y = 6 X
  • 7. 7 (0, 3) (3, 0) (-3, 0) (0, -3) 29.6x ¨C 5y =10 Y (-2, 0) (2, 0) (0, 2) (0, -2) 30. 2x ¨C y = 6 x + 2y + 2 = 0 (-2, 2) (3, -1) (1, -3) (2, -2) 4 !