Question

Consider the systems of equations below.
x+y=6
y=-x+2

Answer 1

how would I graph it tho

Answer 2

Which statement correctly describes the graphs of these equations?
A) the lines are parallel
B) the lines coincide
C) the lines intersect at (2,4)
D) the lines intersect at (-2,8)

Answer 3

help me pls

Answer 4

x + y = 6
y = -x + 6
In y = mx + b form, the m position is the slope. So the slope for this one is -1.

y = -x + 2
The slope for this one is also -1.

If both equations have the same slope, then they are parallel

Answer 5

texaschic101, they can still coincide until you compare the m's.

I'll suggest an alternative method. You want to know where the lines intersect if they do. Assume that they intersect. In the points where they intersect, both equations must be satisfied. Substitute the second equation into the first one to obtain
\[x + (-x + 2) = 6\\2 = 6\]
That's a contradiction so our assumption that the lines intersect is invalid. Thus they are parallel and they do not coincide. Answer A.