How many solutions does the system have?

To find the number of solutions for the given system of equations, we can solve it using any method (substitution, elimination, or graphing) and see how many solutions we obtain.

Let's solve it using the method of elimination. We'll multiply the first equation by 2 to make the coefficients of x in both equations cancel each other out:

2(x + 2y) = 2(2)
2x + 4y = 4

Now, we have the following system of equations:

2x + 4y = 4
2x + 4y = -8

Since the coefficients of x and y are the same in both equations, we can subtract one equation from the other to eliminate x:

(2x + 4y) - (2x + 4y) = 4 - (-8)
0 = 12

The equation 0 = 12 is not possible, which means there are no values of x and y that satisfy both equations. Therefore, the system has no solution or is inconsistent.