Final answer:
To determine if the point (0, 2) is an element of the solution set for the system of equations, we substitute the values of x and y into each equation and see if both equations are true. (0, 2) is not a solution to the first equation but it is a solution to the second equation. Therefore, it is not an element of the solution set for the system of equations.
Step-by-step explanation:
To determine if the point (0, 2) is an element of the solution set for the system of equations, we substitute the values of x and y into each equation and see if both equations are true.
Substituting x=0 and y=2 into the first equation, we have 0 + 37 = 6, which is false. Therefore, (0, 2) is not a solution to the first equation.
Similarly, substituting x=0 and y=2 into the second equation, we have 1 - 0 + 47 = 8, which is true. Therefore, (0, 2) is a solution to the second equation.
Since (0, 2) is not a solution to both equations, it is not an element of the solution set for the system of equations.