Sistemi di equazioni di primo grado a più di due incognite

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Risolvere e discutere i seguenti sistemi:

  1. \bigg \{ \begin{array}{ll} x+y+z=1 \\ 2x+y-z=6 \\ x-y+2z=-5 \end{array}
  2. \bigg \{ \begin{array}{ll} x-y+z=-1 \\ x+2y-z=8 \\ 3x-y+2z=3 \end{array}
  3. \bigg \{ \begin{array}{ll} 2x+y+a=1 \\ 4x-y+z=-5 \\ -x+y+2z=5 \end{array}
  4. \bigg \{ \begin{array}{ll} 3x-y-z=8 \\ x+y=1 \\ 2y-z=-1 \end{array}
  5. \bigg \{ \begin{array}{ll} 3x+2y+z=3 \\ x-y+z=\frac 56 \\ x+y=\frac 56 \end{array}
  6. \bigg \{ \begin{array}{ll} x+2y+z=3 \\ -2x+y-2z=-1 \\ y+z=4 \end{array}
  7. \bigg \{ \begin{array}{ll} \frac 13x-y+z=\frac 32 \\ x+y-2z=0 \\ 2x-z=\frac 52 \end{array}
  8. \bigg \{ \begin{array}{ll} \frac{2y+x-z}3 + \frac 15x=\frac 45 \\ 2y-\frac{x+z}2=3 \\ 2(x-y)-\frac 13z=-2 \end{array}
  9. \bigg \{ \begin{array}{ll} \frac{x-3z}2=y \\ x+6(\frac y3 - \frac z2) = 0 \\ 3x+y=z+1 \end{array}
  10. \bigg \{ \begin{array}{ll} x(z+2)=(x+1)(z+1) \\ (y+4)(x+3)=(x+1)(y+5) \\ (z+2)(y+3)=(z-1)(y+6) \end{array}

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