Lineare Gleichungssysteme

Question

Aufgabe: Wie rechne ich dieses Gleichungssystem?

7x-41=-3y

9x-13y=19

Answer 1

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Answer 2

7x-41=-3y    ==>   -7/3 * x  + 41/3   = y

                      in die 2. einsetzen gibt 
9x-13(-7/3 * x  + 41/3 )=19

<=>   9x+91/3 * x  -533/3 =19   | *3

<=>   27x+91x  -533 =57

<=>   118x =590

<=>       x = 5     also   y = -35/3 + 41/3 = 2

Probe 7*5-41=-3*2  <=>  35-41 = -6  ok

9*5-13*2=19    <=>   45 - 26 = 19  ok

  

Answer 3

7x-41=-3y
9x-13y=19

z.B. Einsetzungsverfahren

-7/3·x+41/3=y

9x-13(-7/3·x+41/3)=19

9x+91/3·x-533/3=19

27x+91x-533=57

118x=590

x=590/118

x=5

35-41=-3y

y=2