Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations:

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

1 answer

To determine the solution to the system of equations, let's first manipulate and compare the two equations. The system is as follows:

  1. 8x2y=4
  2. 4xy=2

We can simplify the first equation by dividing everything by 2:

4xy=2

Now both equations are identical:

  • 4xy=2 (from the second equation)
  • 4xy=2 (the first equation after simplification)

Since both equations are the same, the system has infinitely many solutions along the line defined by 4xy=2.

Thus, the statements that correctly describe the solution to the system of equations are:

  • The system has infinitely many solutions.
  • The two equations represent the same line.

If provided with specific statements to check, you would confirm the above conclusions based on the context given.