Question

how do I solve x + y = 0 and x - y + 2 = 0

Answer 1

Solve for x in the first equation (i.e isolate it):
\(x+y=0 \\
x = 0 - y \\
x = -y \)

Since x = -y in this equation, plug in x = -y into the second equation:
\(x - y + 2 =0 \\
(-y) - y + 2 = 0 \\
-2y + 2 = 0 \\
-2y = 0 - 2 \\
-2y = -2 \\
y = 1 \)

Now you know the value of y, so substitute y = 1 into any equation to find the value of x: I will do this with the first equation:

\(x + y = 0\\
x + 1 = 0\\
x = -1\)

So:
\(\boxed{x=-1, y=1}\)