How do you solve the system x -y = 4 and x + y = 4?

May 21, 2015

The answer's (4, 0), but I'm assuming you want to know how to get that.

The best method to use in this case to solve the system of equations is elimination:

$\left(x + y = 4\right) + \left(x - y = 4\right) = \left(2 x = 8\right)$

If 2x = 8, then x = 4.

Now, plug '4' back into one of the equations for 'x'.

$x + y = 4$
$\left(4\right) + y = 4$
$y = 0$

So, y is 0. Therefore, the solution to this system (the point where the 2 lines cross) is (4, 0).