I arrived in solving problems in linear algebra equations below.But I need to prove that the decision to conclude one of the four following equation is the result of the other three.
Can you help me to prove.....
$$a+b-\lambda(c-a)=0, \\ a\alpha-b-\lambda(d-b)=0, \\ c+d-\lambda c=0, \\ c\alpha-d-\lambda d=0$$
wich $\alpha \gt-1 $ is a constant.