how many solutions will this system have: 2x+y=-6 and y=-2x+8?

Question

i tried doing it myself but got a tad confused, if someone could help me with the step-by-step it would be nice, i can't tell where i went wrong

Answer 1

They would have no points overlapping. if we solve for the first equation we will get

y=-2x-6

We see that both equations have -2 as their slope. The rule is that a solution to a system is where the lines will intersect. Given the equations have the same slope they can be seen as parallel and thus have no point of intersection.

Therefore no solutions possible.