To determine whether the point (0, 3) is a solution to the given system of equations, we need to substitute \(x = 0\) and \(y = 3\) into both equations and check if they hold true.
The first equation is: \[ \frac{1}{3}x + y = 3 \] Substituting \(x = 0\) and \(y = 3\): \[ \frac{1}{3}(0) + 3 = 3 \] \[ 0 + 3 = 3 \] This is true.
Now, let's check the second equation: \[ 2y = -\frac{2}{3}x + 10 \] Substituting \(x = 0\) and \(y = 3\): \[ 2(3) = -\frac{2}{3}(0) + 10 \] \[ 6 = 0 + 10 \] \[ 6 = 10 \] This is false.
Since the second equation is not satisfied by the point (0, 3), we conclude that (0, 3) is not a solution to the system of equations.