Question

How do you find the point of intersection for `x+y= -3` and `x+y=3`?

Answer 1

From `x+y=3->y=-x+3=3-x`

Explanation:

Now substitute that in the other equation:
`x+y=x+(3-x)=-3->3=-3`
This cannot be. Clearly there is no intersection.

We could have seen this, because (as we have seen before), the second equation translates to a slope-intercept form of
`y=-x+3`
While the first will translate to:
`y=-x-3`
Same slope (`-1`), but different intercepts (`+3and-3`), in other words, these are parallel lines.
Here is the graph for `y=-x+3` the other one runs parallel and `6` units below it:
graph{-x+3 [-10, 10, -5, 5]}