If the graph of a system of linear equations results in parallel lines, what can we say about the solution to that system?

Question

saifoo.khan · Answer

Lines are parallel, system is called inconsistent.

anonymous · Answer

the slope of two lines is equal

anonymous · Answer

@saifoo.khan Or we can say that the system of equations are consistent for every possible solution.

directrix · Answer

>what can we say about the solution to that system?

There is no solution to that system.

anonymous · Answer

That's not true. We can't assume the lines have no solution if they are parallel.

directrix · Answer

@Romero >That's not true. 

Why not?

anonymous · Answer

That information alone is not sufficient to conclude there is no solution. Setting up the matrix of a system of equations Ax=b 
Parallel lines tells us that there will be a zero row in A but does not give us information about b.

If the second value for b was a non zero then there will be no solution but if the value of the second b was a zero then we have a system of equations with an infinite number of solutions


Like I said the zero suggest that the system of equations can have no solution of an infinite number of solutions but to assume that the system has no solution is an easy mistake a lot of people make.

anonymous · Answer

@directrix