First we are going to express both equation in terms of [tex]y[/tex] to compare their slopes:
For our first equation:
[tex]-x=1-y[/tex]
[tex]-x-1=-y[/tex]
[tex]y=x+1[/tex]
For our second equation:
[tex]-1+y=x+2[/tex]
[tex]y=x+3[/tex]
So now we have our system of equations in terms of y:
[tex] \left \{ {{y=x+1} \atop {y=x+3}} \right. [/tex]
Notice that the slope, the coefficient of [tex]x[/tex], in both equations is the same: 1, and if tow linear equations have the same slope, they are parallel.
We can conclude that we can classify the system of equations as parallel.
