A linear system has an infinite number of solutions if the two equations describe the SAME line.
Example: y = 2x and 4x - 2y = 0. The equation 4x - 2y = 0 can be solved for y by adding 2y to both sides and then dividing by 2:
[tex]4x-2y=0 \\ 4x=2y \\ 2x=y[/tex]
The "two" lines are really the same line, so the system has an infinite number of solutions.
Your system is y = 4x and 4x + y = 0. Is the second equation equivalent to the first?
[tex]4x+y=0 \\ y=-4x[/tex]
No! The statement is false.
