Let's take each pair of points and find the slope of the line that connects them.
For each pair of points let's call the first one [tex]( y_{2} , x_{2} )[/tex] and the second [tex]( y_{1} , x_{1} )[/tex].
We then substitute into the formula for the slope which is: [tex]m= \frac{ y_{2} - y_{1} }{ x_{2} - x_{1} } [/tex]
FIRST PAIR OF POINTS [tex]m= \frac{1-1}{ 4-0}=0 [/tex]
SECOND PAIR OF POINTS [tex]m= \frac{-4-4 }{ 0-4}=2 [/tex]
If two line have the same slope they are parallel and do not meet. These have different slopes so they are not parallel and will intersect at a point. That point gives the one solution to the system.
