The system of equations 2y = 6x + 8 and y = 3x + 4 has infinitely many solutions.
To determine the number of solutions for the system of equations 2y = 6x + 8 and y = 3x + 4, we can set the two equations equal to each other:
2y = 6x + 8
y = 3x + 4
By substituting the value of y from the second equation into the first equation, we get:
2(3x + 4) = 6x + 8
6x + 8 = 6x + 8
Simplifying the equation, we get:
6x + 8 = 6x + 8
0 = 0
This equation is true for all values of x.
Therefore, the two equations are equivalent and intersect at every point.
This means that the system of equations has infinitely many solutions.