Given the following system of equations, identify the type of system. \( \begin{array}{l}x+y=6 \\ y=3-x \\ \text { inconsistent } \\ \text { equivalent } \\ \text { consistent }\end{array} \)

These equations represent a consistent system. To see why, let’s solve the system. The first equation, \(x + y = 6\), can be rearranged as \(y = 6 - x\). The second equation already states \(y = 3 - x\). By substituting \(y\) from the second equation into the rearranged first equation, we can set up \(3 - x = 6 - x\). Since both equations describe lines in the same plane and intersect at a point, this system is termed consistent because it has at least one solution. The system also demonstrates that it is not inconsistent since an inconsistent system would imply the equations are parallel and do not intersect. If we plot both equations, we can clearly see that they meet at the point (3, 3), indicating this system indeed contains solutions and is consistent!