x+y=10    y=x+2

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y = x + 2  - its terms can be moved around so that it becomes -x + y = 2. Then you subtract this equation from the first one, x + y = 10. x - (-x) = 2x, y - y = 0y, and 10 - 2 = 8. We've eliminated the y, so we only have one unknown variable to solve for right now. 2x = 8. You divide 2x by 2 and 8 by 2, and you get x = 4. Now we solve for y. I'm going to pick the first equation, though it doesn't really matter. 4 + y = 10. y = 6. Your solution is x = 4, y = 6.