Question

When solving a system of linear equations algebraically, how do you know when the system has no solution? Infinitely many solutions?

Answer 1

You know that the system of equations has no solution because you get something funky when trying to solve for x like:

`7 = 25`
This happens because the system dont intersect.
Now there are infinite number of solutions when its the same equation (it may look different because it was multiplied by a scalar).
But in general, you will get something like

`7 = 7`
If you have any questions feel free to ask!