The equations x + y = 5 and 2x + 2y = 10 describe the same line. If a third equation, x - y = 1, is added to form a system of three…

The second equation, $2x + 2y = 10$, is just the first equation $x + y = 5$ multiplied by 2, so it adds no new information. The system effectively consists of $x + y = 5$ and $x - y = 1$. Add them: $2x = 6$, so $x = 3$, and then $y = 2$. Check in all three equations: $3 + 2 = 5$, $6 + 4 = 10$, and $3 - 2 = 1$. A common wrong answer is 2, which is the value of $y$, and another is 5 or 6, which result from not eliminating $y$ properly or stopping at $2x = 6$.