Find $\lambda$ and solve the matrix

Question

Find $\lambda$ and solve the matrix. I have 4 equations:

\begin{cases} x+y+z-t=2\\ x+y-z+t=2\\ 3x+y+z+t=\lambda\\ x-y+z+t=2\\ \end{cases} I've got $$t=\frac{\lambda -6}{4}; \ z=\frac{6-\lambda}{4};\ y=\frac{\lambda -6}{4}; \ x=\frac{2+\lambda}{4}$$

What I did wrong?

Answer 1

After adding of the first, second and forth equations we'll get $$3x+y+z+t=6,$$ which gives $\lambda=6.$

Answer 2

Hint: It is $$x=2-t,y=t,z=t$$ and $$\lambda=6$$

Answer 3

Subtracting eq. 2 from both eq. 1 and eq. 4 gives \begin{cases} 2z-2t=0\\ x+y-z+t=2\\ 3x+y+z+t=\lambda\\ -2y+2z=0\\ \end{cases} Which implies $$\begin{cases} z=t\\ x=2-y\\ 6-3y+3y=\lambda\\ y=z=t\\ \end{cases}\implies \lambda = 6$$