your equation becomes:
-(x - y) = -x + y
simplify to get -x + y = -x + y
add x to both sides of the equation and subtract y from both sides of this equation to get:
-x + x + y - y = -x + x + y - y, which results in:
0 = 0
since all the variables disappeared from the equation and the equation is true, this means that any values of x and y will satisfy the original equation.
in other words, the equation is an identity.
for example:
let x = 15 and y = 20 (numbers off the top of my head).
-(x - y) = -x + y becomes:
-(15 - 20) = -15 + 20
simplify to get:
-15 + 20 = -15 + 20
it's plain to see that this equation is true.
if you add 15 to both sides of this equation and subtract 20 from both sides of this equation, you will get:
0 = 0
now to graphing this equation.
what i find is that it doesn't graph on a 2 dimensional plane.
it does graph on a 3 dimensional planes and the result is that z = 0.
on a 2 dimensional plane, you start out with:
-(x-y) = -x + y
to graph this, you solve for y.
start with -(x-y) = -x + y
simplify to get -x + y = -x + y
add x to both sides of this equation and subtract y from both sides of this equation to get:
0 = 0.
there's nothing to graph.
on a 3 dimensional plane, you get:
z1 = -(x - y)
z2 = -x + y
set z = z1 - z2.
this becomes z = -(x - y) - (-x + y) which becomes z = -x + y + x - y which becomes z = 0.
the 3 dimensional graph is a plane at z = 0.
this means that any value of x and y will make z = 0.
the 2 dimensional graph will show nothing.
the 3 dimensional graph will show z = 0.
here's what the 3 dimensional graph will look like.
the plane is empty which means that any value of x and y will satisfy the equation.