(Solved):   (b) only please 3. ( 4 marks) For each of the following linear systems, with real variables ...

 

(b) only please

3. ( 4 marks) For each of the following linear systems, with real variables \( x_{1}, \ldots, x_{6} \) and \( y_{1}, \ldots, y_{4} \) respectively, state how many solutions the system has. Note that the systems have already been written in echelon form. You do not need to find the solutions. (a) \[ \begin{aligned} x_{1}+x_{2}+x_{3}+x_{4}+x_{6} &=3 \\ 2 x_{2}-x_{4}+x_{5} &=0 \\ 3 x_{4}+x_{6} &=3 \\ x_{6} &=1 \end{aligned} \] (b) \[ \begin{aligned} y_{1}+y_{2}+y_{4} &=2 \\ -y_{2}+y_{3} &=1 \\ y_{3}+y_{4} &=1 \\ y_{4} &=0 \end{aligned} \]