I: y=2|x|+8
II:2x+y=8
with II:
2x+y=8
y=8-2x=-2x+8
so how many solutions are there?
for I by itself there are infinite solutions like y=8, x=0 or y=10,x=1 and so on, for any x we can find a matching y
and II is very similar
do these infinite solutions also exist in I and II?
set them equal:
I=II
2|x|+8=-2x+8
2|x|=-2x
|x|=-x
it doesn't work for x>0 because then the left side is >0 and the right <0, but for example x=0, x=-1, x=-2 (in general all x<=0) are part of the solution set, which means there is also an infinite amount of valid "-3x" values
so yes there is an infinite amount of solutions for the system of equations
