Question

Is the equation x=-5-y and 2+y=-x+3 coincident, intersecting, or parallel

Answer 1

Well first, you have to get both equations to the y= form
y=mx+b

X=-5-y   add y to x

y+x=-5   then subtract x

y=-x-5     is your equation
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for the second one:

2+y=-x+3    subtract 2

y=-x+1         is your equation
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Take both equations and compare:

Both the slopes are the same of -x, so that means the will lines never touch (also because of different y intercept)

So, the answer is parallel.