If a have a linear system of three equations in three unknowns but two of the three equations are multiples of each other, does it mean the linear system has infinitely many solutions? Why?
Linear equations of 3 variables represent planes in a 3D space.
If you have two distinct planes in a 3D space they intersect along a line(if they aren't parallel). Now if you have a third plane then that would intersect with this line on a single point. Or if the line is parallel it might not.
Since you two equations in that are multiples of each other then that means that they represent the same plane in the 3D space. And two planes would always intersect at a line if they aren't parallel. Since a line has infinitely many points there are infinitely many solutions to this.