To determine the number of solutions to the system of equations, we can first rewrite the equations.
The first equation is:
- \( 2x + y = 6 \)
The second equation is:
- \( 4x + 2y = 8 \)
Now, let's simplify the second equation by dividing all terms by 2:
\[ \frac{4x}{2} + \frac{2y}{2} = \frac{8}{2} \] Thus, the second equation simplifies to:
\[ 2x + y = 4 \]
Now we can see the two equations we have:
- \( 2x + y = 6 \)
- \( 2x + y = 4 \)
Next, we observe that the left sides of both equations are identical (both are \( 2x + y \)). However, the right sides are different (6 and 4). This means the two equations represent parallel lines, which never intersect.
Since the lines do not intersect, there are no solutions to this system of equations.
Thus, the answer is:
0