Without graphing is the system independent, dependent, or inconsistent?

y = 2x - 8
2x - y = 8

Question

Without graphing is the system independent, dependent, or inconsistent?

y = 2x - 8
2x - y = 8

anonymous · Answer

since both equations are same and there is no added variable hence the equation is independent .

debbieg · Answer

THIS system is NOT independent.

A dependent system is one that has infinite solutions - because the two equations are really the SAME equation, hence the same line, and hence every point on the line is a solution to both equations. It is easy to spot a dependent system if one equation is a multiple of the other, or if one is simply a rearrangement of the other.

The system is inconsistent if the two equations are parallel lines. Easy to spot if you solve each for y, and you get the same slope with different y-intercepts. Or, if you try to solve by elimination, and get a false statement of equality (like, 2=0).