How would you be able determine if a system of linear equations has no solution without actually solving it?

You need to solve it. When it has infinately many solutions it means you can plug in any number and you will get the same answer. ex: 0x=0 simple but I hope it helps.

I guess you'll have to solve it O_O

If the equation is like 2x+5=5+2x that would have infinite numbers (but this is not linear equation)

If you mean the solution as a slope

straight horizontal line has 0 slope

and straight vertical line has no solution
sorry it may not help O_O

you need n number of unique equations to solve n number of unknowns.

when there are more unknowns then unique equations you get infinitely many solutions.

for example
equation 1: 2x - 6y = 0
equation 2: 4x -12y = 0

these two equations are different equations but they are not unique. the second equation is just a multiple of the first.

There is a method of knowing it's solvable or not. First find the determinant if it is 0 then the linear equations has no unique set of solution.

(to find the determinant put the linear equation into matrix form: for the above example
det |2   -6|
...... |4 -12| = 0

thus it has infinitely many solutions.