Linear EQUATIONS

[kathy's]

I am really confused about one thing of linear equations do all linear equations have solutions?can someone give me an example and explain it to me but my teacher want me to know it with no ordered pair satifying it.

 

[Unco]

Example:

-x - 2y - 1 = 0 [1]
2x + 4y - 3 = 0 [2]

Try to solve the system.

Add 2*[1] to [2] and we have -5 = 0.

This is a false statement; there is no coordinate that makes both equations true -- there is no solution.

Why?

Rearrange each equation to the form y = mx + b:

[1]: y = -x/2 - 1/2

[2]: y = -x/2 + 3/4

Notice that m = -1/2 for both --> the lines have the same slope (and are not the same line) so they are parallel <--> they do not intersect.