Question

how can you tell if a systems of equations has no solution?

Answer 1

They lines never intersect.

Answer 2

They never meet.
In other words, their slope is same but y-intercepts are different.

Answer 3

A system of equations will have no solution if you run into a contradiction. For example, if you have one equation telling you that y=x+1, and another telling you that y=x-1, they can't both be true. It's a contradiction, so there must be no solution.

Answer 4

convert the system into an augmented matrix,if the ranks are not equal you won't get solution to the given system.

Answer 5

What? If you convert it into an augmented matrix, that matrix will have a rank. Each equation won't have its own rank. And if you're looking for the condition for there not being a solution, you're looking for a row of zeros with a non-zero term in the augmented portion of the matrix. Which, coincidentally, is the same as my suggestion of looking for a contradiction.

Answer 6

let Ax=b is the system of equations in the matrix form. augmented matrix is A|b,
if rank(A)≠rank(A|b)
this system of equations have no solutuon.

Answer 7

Okay, I see what you mean. The rank of the matrix is different from the rank of the augmented matrix. The way that you initially phrased that was really unclear.

Answer 8

i'm really sorry about that