What is the \( x \)-coordinate of the solution of the following system of equations? \( \begin{array}{l}3 x+y=6 \\ x-y=6 \\ 3\end{array} \) -3

To determine the \( x \)-coordinate of the solution to the system of equations, we can solve the two equations: 1. From the first equation, \( 3x + y = 6 \), we can express \( y \) in terms of \( x \): \[ y = 6 - 3x \] 2. Now, substitute \( y \) into the second equation \( x - y = 6 \): \[ x - (6 - 3x) = 6 \implies x + 3x - 6 = 6 \implies 4x - 6 = 6 \] \[ 4x = 12 \implies x = 3 \] Thus, the \( x \)-coordinate of the solution is \( 3 \).