Question

How do you know that a system has no solution

Answer 1

A system of equations has no solution when the graphed lines are parallel.

Since parallel lines never intersect, there can be no solution. Systems of equations that have no solution are classified as inconsistent.

Answer 2

A system has no solution if the variable you're looking for completely cancels out. Something like this: x - 3 = x + 4. If we bring over an x to combine it with the other x, x - x = 0 and the x's are gone. And of course- 3 does not equal 4.