2. Identify the number of solutions to the system of equation:

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

1 answer

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.