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Beliebt Algebra >

5x_{1}+7x_{2}=3,2x_{1}+4x_{2}=1

Lösung

5 x_{1} + 7 x_{2} = 3, 2 x_{1} + 4 x_{2} = 1

Lösung

x_{1} = \frac{5}{6}, x_{2} = - \frac{1}{6}

Schritte zur Lösung

[5 x_{1} + 7 x_{2} = 3 2 x_{1} + 4 x_{2} = 1]

Stelle

x_{1}

nach

5 x_{1} + 7 x_{2} = 3

um:

x_{1} = \frac{3 - 7 x _{2}}{5}

Ersetze

x_{1} = \frac{3 - 7 x _{2}}{5}

[2 \cdot \frac{3 - 7 x _{2}}{5} + 4 x_{2} = 1]

Vereinfache

[\frac{6 + 6 x _{2}}{5} = 1]

Stelle

x_{2}

nach

\frac{6 + 6 x _{2}}{5} = 1

um:

x_{2} = - \frac{1}{6}

Für

x_{1} = \frac{3 - 7 x _{2}}{5}

Ersetze

x_{2} = - \frac{1}{6}

x_{1} = \frac{3 - 7 ( - \frac{1}{6} )}{5}

\frac{3 - 7 ( - \frac{1}{6} )}{5} = \frac{5}{6}

x_{1} = \frac{5}{6}

Die Lösungen für das Gleichungssystem sind:

x_{1} = \frac{5}{6}, x_{2} = - \frac{1}{6}

Graph

Beliebte Beispiele

2y-x=-9,7y-2x=3

2 y - x = - 9, 7 y - 2 x = 3

3x+5y=38,3x-y=-4

3 x + 5 y = 38, 3 x - y = - 4

11x+5y=7,6x-3y=21

11 x + 5 y = 7, 6 x - 3 y = 21

x+3y=12,3x+2y=123

x + 3 y = 12, 3 x + 2 y = 123

7x-3y=31,9x-5y=41

7 x - 3 y = 31, 9 x - 5 y = 41