Why is there unique plane which passes through given point and is parallel to given line I was trying to solve one question which is asking to find a plane which passes through given point and is parallel to given line.
The given point is $M(2,-5,3)$ and the given line is given as an interesection of the planes $2x-y+3z-1=0 \text{ and } 5x+4y-z-7=0$
It is still unclear for me why there is only one unique plane which can be answer, I think that there are more possible planes that can be answers to this.

As another answer points out, the claim is false.  Given a set of planes parallel to each other as well as to the given line, only one of those planes will pass through the given point.
