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

Question

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

Answer 1

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

1. \( 8x - 2y = -4 \)
2. \( 4x - y = -2 \)

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

\[ 4x - y = -2 \]

Now both equations are identical:

• \( 4x - y = -2 \) (from the second equation)
• \( 4x - y = -2 \) (the first equation after simplification)

Since both equations are the same, the system has infinitely many solutions along the line defined by \( 4x - y = -2 \).

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.