Bestimmung der Lösungsmenge

Question

Aufgabe:

\( \left|\begin{array}{c}11 x-7 y=3 x+2 y+22 \\ 8 x+3 y=5 x+8 y+5\end{array}\right| \)

Lösungswege IL bestimmen ?

Freue mich über Antworten

Answer 1

Hallo,

1) 11x-7y=3x+2y +22 |-3x-2y

1)8x-9y=22

2) 8x+3y=5x+8y +5 |-5x-8y

2)3x-5y=5

----->

1) 8x-9y=22  |*3
2 )3x-5y=5    |*8
---------------------
1)24x -27y=66
2)24x -40y=40
-------------------
1-2: 13y= 26  ---->y=2
in z.B 1)

8x-9y=22
8x- 18=22
8x=40
x=5

L = (5/2)

Answer 2

Hallo,

erst sortieren

11x- 7y = 3x+2y+22             8x -9y =22      |*3                  24x -27y = 66

8x+3y = 5x+8y+5                 3x -5y= 5        | *(-8)           -24x +40y  = -40      | I´´. +I´´ addieren

                                                                                         0 +13y = 26         y= 2       in I. oder II einsetzen

                                                                                   11x -14= 3x +4+22     x= 5

       L = { 2 .5}

                                                          

                                                                                    

Answer 3

11·x - 7·y = 3·x + 2·y + 22
8·x + 3·y = 5·x + 8·y + 5

8·x - 9·y = 22
3·x - 5·y = 5

8*II - 3*I

- 13·y = -26 → y = 2

Jetzt noch einsetzen

3·x - 5·2 = 5 → x = 5