Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations: 8x−2y=−4 4x−y=−2 (2 points) Responses Solve this system by elimination since it is already in standard form and lined up nicely. Solve this system by elimination since it is already in standard form and lined up nicely. There is exactly one solution to this system of linear equations and it is (2, 0). There is exactly one solution to this system of linear equations and it is (2, 0). There are infinite solutions to this system of linear equations. There are infinite solutions to this system of linear equations. These lines are parallel, so there is no solution to this system of linear equations. These lines are parallel, so there is no solution to this system of linear equations. There is exactly one solution to this system of linear equations and it is (0, -2). There is exactly one solution to this system of linear equations and it is (0, -2). Solve this system by substitution since one of the variables is defined by the other without having to do any math..

Answer 1

To analyze the system of equations:

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

Let's simplify both equations and see if they represent lines that intersect, are parallel, or are the same line.

First, we can manipulate the second equation to express \( y \) in terms of \( x \):

From the second equation:
\[ 4x - y = -2 \]
\[ y = 4x + 2 \]

Now, we can manipulate the first equation to also express \( y \) in terms of \( x \):

From the first equation:
\[ 8x - 2y = -4 \]
Divide everything by 2:
\[ 4x - y = -2 \]

Notice that the first equation simplifies exactly to the second equation. Thus, both equations represent the same line.

This means that there are infinitely many solutions because any point on this line will satisfy both equations.

Correct statements:

• There are infinite solutions to this system of linear equations.
• Solve this system by elimination since it is already in standard form and lined up nicely (though in this case, you would recognize they are the same equation).

The incorrect statements would be those that suggest there is exactly one solution or that the lines are parallel or distinct.