Question

Select the statement that correctly describes the solution to this system of equations.

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

Responses

There are infinitely many solutions.
There are infinitely many solutions.


There is no solution.
There is no solution.

There is exactly one solution at (0,–2).
There is exactly one solution at (0,–2).


There is exactly one solution at (2,0).

Answer 1

To determine the relationship between the two equations and find the solution, let's analyze them:

The two equations you provided are:

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

First, we can simplify the first equation. Divide the entire equation by 2:

\[ 4x - y = -2 \]

Now we see that the first equation simplifies to the second equation:

\[ 4x - y = -2 \]

Since both equations are identical, this means they represent the same line. Therefore, every point on this line is a solution to the system of equations, which indicates that there are infinitely many solutions.

Thus, the correct statement is:

**There are infinitely many solutions.**