Answer:
[tex]y=-6x-2, y=-6x-2[/tex]
infinitely many solutions : The equations are identical, so the lines are exactly the same. Therefore, every coordinate pair on the line is a solution to both equations.
(this is called a dependent system)
[tex]y=0.5x+5, y=0.5x+1[/tex]
no solutions : The two lines have the same slope (gradient), therefore they are parallel and will never intersect.
(this is called an inconsistent system)
[tex]y=0.25x-2,y=5x-4[/tex]
one solution : The lines intersect at only one point.
(this is called an independent system)
[tex]y=2x+3,y=4x-1[/tex]
one solution : The lines intersect at only one point.
(this is called an independent system)
[tex]y=2x+1.5, y=2x+1.5[/tex]
infinitely many solutions : The equations are identical, so the lines are exactly the same. Therefore, every coordinate pair on the line is a solution to both equations.
(this is called a dependent system)
[tex]y=-x-3, y=-x+3[/tex]
no solutions : The two lines have the same slope (gradient), therefore they are parallel and will never intersect.
(this is called an inconsistent system)
