I have a system of equations shown as below:
$x_1x_3+x_5 = a$
$x_2 x_3 +x_5 =c$
$x_2x_4 +x_5 =d$,
where $x_1,x_2,x_3,x_4,x_5$ are variables and $a,b,c,d$ are constant.
Given any $(a,b,c,d)$, is it always possible to find a valid solution?
For example, given $a=1,b=c=d=0$, I can find a solution as $x_1=x_3=1,x_2=x_4=x_5=0$.
This is not a homework problem that I'm trying to find an answer. I just don't know where to start to tackle this problem. Can someone provide some hints?
Please check if this statement is right: If $b-a = d-c \neq 0$ and ($a\neq c$ or $b\neq d$), then there is no solution; otherwise, there is always a solution.