How to solve this equation system?

Question

$2x-2y+2=0 $

$-2x+2y-2=0 $

So, from the second one I get that $2 (-x+y)=2 $ which takes me to think that $-x+y=1 $

However, that's how far I get. How can I find an exact x or y value?

Answer 1

You can't: the first equation says the same thing as the second, so the relationship between x and y you got is as far as you can get.

Are you sure you got the right equations?

Answer 2

Unfortunately, your given system of equation has no singular - exact - $x$ or $y$ value. It does have a definable multitude of answers, however.

If we multiply both sides of the first equation by $-1$:

$$-(2x-2y+2)=-0$$

$$-2x+2y-2=0$$

by the Distributive Property. This is the second equation, so the first and second equations really mean the same thing.

As you have shown, $-x+y=1$. That means that we are looking for all solutions $(x,y)$ to that equation. With some simple manipulation we find that

$$-x+y=1$$

$$y=x+1$$

and so any pair $(x,y)$ where $y=x+1$ will work. For example,

$(x,y)=(4,5)$ and

$(x,y)=(5+\pi,6+\pi)$

are both perfectly valid solutions to the problem.

How you format this, however, depends on the given question.