Alright, let's go through our ordered pairs one by one and substitute them into the given equation, 2y=6x+4, to see whether they satisfy it.
1. The first ordered pair is (1, 5). This means x=1 and y=5. So if we substitute these values into our equation, we get 2*5 = 6*1+4. Simplifying that gives us 10=10, which is true. So the first pair, (1,5), is a solution to the equation.
2. The second pair, (7, -47), suggests x=7 and y=-47. Substituting these in gives 2*(-47) = 6*7+4, simplifying to -94 =42 + 4 = 46. This is not true. So, (7, -47) does not satisfy the equation.
3. Lastly, the pair (0, 47). This would give x=0 and y=47, so our equation is 2*47 = 6*0+4, simplifying further to 94 = 4, which obviously is not correct. Thus, the pair (0, 47) does not satisfy the equation.
After examining all three pairs, we find only the first pair, (1,5), is a solution to the equation 2y=6x+4.