To find the number of solutions to the system of equations, we can solve the equations using any method (substitution, elimination, etc.) and see if we end up with a unique solution, infinitely many solutions, or no solution.
First, let's solve the system of equations using the method of substitution.
From the first equation, we can rewrite it as:
y = 2x - 4
Now we can substitute this expression for y in the second equation:
-4x + 2(2x - 4) = 2
-4x + 4x - 8 = 2
-8 = 2
This is a contradiction! The equation -8 = 2 is not true, so there is no solution to the system of equations.
Therefore, the number of solutions to the system of equations is 0.
2. Identify the number of solutions to the system of equation:
2x = y + 4
-4x + 2y = 2
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