Solve the system of equations. y = -x + 10 y = x + 2 (2,-6) (4,6) (6,2) (4,-6)

To solve the system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

The system of equations is:

1. y = -x + 10
2. y = x + 2

We can solve this system by setting the two equations equal to each other, since they both equal y:

-x + 10 = x + 2

Now, we can solve for x:

Add x to both sides to get 10 = 2x + 2.

Subtract 2 from both sides to get 8 = 2x.

Divide both sides by 2 to get x = 4.

Now that we have x, we can substitute it into the first equation to find y:

y = -(4) + 10 = 6

So, the solution to the system of equations is (4,6).