To determine if \((0, 3)\) is a solution to the system of equations, we need to substitute \(x = 0\) and \(y = 3\) into both equations and check if they hold true.
Equation 1: \[ \frac{1}{3}x + y = 3 \] Substituting \(x = 0\) and \(y = 3\): \[ \frac{1}{3}(0) + 3 = 3 \] This simplifies to: \[ 0 + 3 = 3 \] This is true.
Equation 2: \[ 2y = -\frac{2}{3}x + 10 \] Substituting \(x = 0\) and \(y = 3\): \[ 2(3) = -\frac{2}{3}(0) + 10 \] This simplifies to: \[ 6 = 0 + 10 \] This simplifies to: \[ 6 = 10 \] This is false.
Since \((0, 3)\) satisfies the first equation but not the second, it is not a solution to the system of equations.