Given the following system of equations, tell me if there are infinitely many solutions, sometimes, or never. Explain your reasoning. y - 2x = 4 and 2y = 4x + 8

Answer 1

To determine if there are infinitely many solutions, sometimes, or never, we can rewrite the second equation in terms of y:

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

Now we can compare the coefficients of x in both equations:

The coefficient of x in the first equation is -2.
The coefficient of x in the second equation is 2.

Since the coefficients of x are NOT equal, we can conclude that the system of equations represents two lines with different slopes. Two lines with different slopes will intersect at a single point, meaning they have only one solution.

Therefore, the system of equations has never infinitely many solutions or sometimes as their intersection results in a single unique solution.