Question

If there is no solution to a graph of a system of equations, then the lines must be?

Answer 1

Parallel

Explanation:

I think this refers to two lines representing a pair of simultaneous equation.

Normally, we do get a solution to set of simultaneous equations, which means they intersect.

Sometimes we get `0=0`, which shows that they actually represent same equation. This is also called by some as two coincident lines having infinite solutions.

Sometimes we also get `k_1=k_2`, where they are non-zeros and not equal, which can also be written as say `k=0`, where `k_1-k_2=0` or say `k=0` where `k!=0`. This means no solution and the two lines are parallel as they do not intersect .