From the graph shown, determine the solution to the system. Write the solution as an ordered pair. \( \begin{array}{l}x+y=6 \\ y=2 x+3\end{array} \)

To find the solution to the system of equations given by \(x + y = 6\) and \(y = 2x + 3\), we can graph both equations. First, for \(x + y = 6\), we can rewrite it as \(y = 6 - x\). This line has a slope of -1 and a y-intercept at (0, 6). For \(y = 2x + 3\), this line has a slope of 2 and a y-intercept at (0, 3). Now, we can find the intersection of these two lines to determine the ordered pair solution. Setting \(6 - x = 2x + 3\): 1. Rearrange the equation: \(6 - 3 = 2x + x\) 2. This gives us: \(3 = 3x\) 3. Solving for \(x\) yields: \(x = 1\) Now, substitute \(x = 1\) back into one of the original equations, using \(y = 2x + 3\): \(y = 2(1) + 3 = 5\) Thus, the solution to the system of equations as an ordered pair is \((1, 5)\).