TeX Quellcode:

\begin{array}{crcrcrcrl} \text{I} & 4x &+& 2y &-& z &=& 1 \cr \text{II} & -8x &-& 6y &+& 8z &=& -13 \cr \text{III} & -4x &+& 10y &-& 5z &=& 9 \cr \cr \text{I} & 4x &+& 2y &-& z &=& 1 \cr \text{2I+II} & & & -2y &+& 6z &=& -11 \cr \text{I+III} & & & 12y &-& 6z &=& 10 \cr \cr \text{I} & 4x &+& 2y &-& z &=& 1 \cr \text{II'} & & & -2y &+& 6z &=& -11 \cr \text{II'+III'} & & & 10y & & &=& -1 & \Rightarrow y = -\dfrac{1}{10} \cr \cr \cr y = -\frac{1}{10} \text{ in II'} & & & -2\cdot \left( -\dfrac{1}{10} \right) &+& 6z &=& -1 & \Rightarrow z = -\dfrac{28}{15} \cr \cr y = -\frac{1}{10} \text{ und } z = -\frac{28}{15} \text{ in I} & 4x &+& 2\cdot \left( -\dfrac{1}{10} \right) &-& \left(-\dfrac{28}{15}\right) &=& 1 & \Rightarrow x = -\dfrac{1}{6} \end{array}