[ Systems of Linear Equations ]

Solve the systems

a) $\left\{\begin{aligned} x-3 y+2 z-t & =3 \\ 2 x+4 y-3 z+t & =5 \\ 4 x-2 y+z+t & =3 \\ 3 x+y+z-2 t & =10\end{aligned}\right.$

b) $\left\{\begin{aligned} x+2 y+3 z-t & =0 \\ x-y+z+2 t & =4 \\ x+5 y+5 z-4 t & =-4, \\ x+8 y+7 z-7 t & =-8 ;\end{aligned}\right.$

c) $\left\{\begin{aligned} x+2 y+3 z & =2, \\ x-y+z & =0, \\ x+3 y-z & =-2, \\ 3 x+4 y+3 z & =0 ;\end{aligned}\right.$

d) $\left\{\begin{aligned} x+2 y+3 z-t & =0, \\ x-y+z+2 t & =4, \\ x+5 y+5 z-4 t & =-4, \\ x+8 y+7 z-7 t & =6 .\end{aligned}\right.$
б) The last two equations follow from the first two.

в) The last equation is equal to the sum of the other three.

## Oтвет

а) $(2,-1,-3,-4)$; б) $(6+5 u-7 v, 2 u, 3 v-3 u, 2 v)$; в) $(-1,0,1)$; г) no solutions.

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