\[ \begin{array}{l}\quad x-3 y=7 \\ 3 y=9\end{array} \] If \( (x, y) \) is the solution to the given system of equations, what is the value of \( x \) ? A) -2 B) 10 C) 16 D) 34

To solve the system of equations, we can start by solving the second equation \(3y = 9\). By dividing both sides by 3, we find that \(y = 3\). Next, we substitute \(y = 3\) into the first equation \(x - 3y = 7\): \[ x - 3(3) = 7 \\ x - 9 = 7 \\ x = 7 + 9 \\ x = 16 \] Thus, the value of \(x\) is \(16\), so the correct answer is C) 16. Now, let’s sprinkle in some extra knowledge! When solving systems of equations, it’s often useful to employ methods such as substitution or elimination. In this case, substitution made it easy to find \(y\) and then solve for \(x\). Also, systems of equations can be represented graphically where the solution is the point where the lines intersect. In this case, the lines represented by the equations would cross at the point \((16, 3)\). Isn’t geometry just the best way to visualize math?