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

Jul 8, 2015

From $x + y = 3 \to y = - x + 3 = 3 - x$

#### Explanation:

Now substitute that in the other equation:
$x + y = x + \left(3 - x\right) = - 3 \to 3 = - 3$
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 ($+ 3 \mathmr{and} - 3$), 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]}