Answer:
The number of solutions of the system is zero
Step-by-step explanation:
we have
a) [tex]x+y=2[/tex]
Isolate the variable y
[tex]y=-x+2[/tex] ----> equation A
This is the equation of the line in slope intercept form
where
The slope is m=-1
The y-intercept is b=2
b) [tex]2x+2y=8[/tex]
Isolate the variable y
[tex]2y=-2x+8[/tex]
[tex]y=-x+4[/tex] ----> equation B
This is the equation of the line in slope intercept form
where
The slope is m=-1
The y-intercept is b=4
Remember that
If two lines are parallel, then their slopes are the same
In this problem the lines A and B are parallel lines with different y-intercept
so
The lines don't intersect
therefore
The system has no solution
