It works well to put both equations in the same form. Here, we use "general form". Any common factors are removed from the numbers. The leading coefficient is positive.
The equations are inconsistent if the x and y coefficients have the same ratio but the constants are different. They are consistent otherwise.
1. 8x +y +4 = 0
.. 8x +y +4 = 0
"consistent" . . . . . and also "dependent"
2. 7x +2y +6 = 0
.. 7x +2y +1 = 0
"inconsistent"
3. x +y +3 = 0
.. x +y +3 = 0
"consistent" . . . . . and also "dependent"
4. x -2y -7 = 0
.. x +3y -7 = 0
"consistent" . . . . . (x, y) = (7, 0)
5. 2x -y +5 = 0
.. 2x -y -2 = 0
"inconsistent"
