What is the result of adding the system of equations? \( \begin{array}{l}2 x+y=4 \\ 3 x-y=6 \\ x=10 \\ x=2 \\ 5 x=10\end{array} \)

The equations you've provided include contradictory statements about the value of \(x\). Solving the first two equations, \(2x + y = 4\) and \(3x - y = 6\), simultaneously gives us a specific result. However, your last three equations suggest \(x\) could be 10, 2, or 2 again (from \(5x = 10\)), which creates confusion. If we take the first two equations alone and eliminate \(y\), we can add them: 1. Adding \(2x + y = 4\) and \(3x - y = 6\): \((2x + y) + (3x - y) = 4 + 6\) results in \(5x = 10\). 2. Dividing both sides by 5, we find \(x = 2\). Substituting \(x = 2\) back into either equation lets us find \(y\): From \(2(2) + y = 4\), we get \(4 + y = 4\) hence \(y = 0\). So, the solution for this consistent system is \(x = 2\) and \(y = 0\), while the others are invalid or inconsistent with this result!