Which equation describes an infinite solution system with the equation y=4x−3

Question

?(1 point)
Responses

2y−8x=6
2 y minus 8 x equals 6

2y+8x=−6
2 y plus 8 x equals negative 6

−2y+8x=−6
negative 2 y plus 8 x equals negative 6

2y−8x=−6
2 y minus 8 x equals negative 6

Answer 1

To find an equation that describes an infinite solution system with the equation \( y = 4x - 3 \), we need to find an equation that is equivalent to this one.

Starting with the given equation \( y = 4x - 3 \), we can rewrite it in standard form (Ax + By = C):

1. Rearrange \( y = 4x - 3 \) to get: \[ -4x + y = -3 \] or \[ 4x - y = 3 \]

Now let's check each of the provided responses to see if they are equivalent to one of these forms:

1. \( 2y - 8x = 6 \)
   Dividing this entire equation by 2 gives: \[ y - 4x = 3 \] This can be rearranged to: \[ 4x - y = -3 \] (not equivalent).

2. \( 2y + 8x = -6 \)
   Rearranging gives: \[ 2y = -6 - 8x \] or \[ y = -4x - 3 \] (not equivalent).

3. \( -2y + 8x = -6 \)
   Rearranging gives: \[ -2y = -6 - 8x \] or \[ 2y = 8x + 6 \] or \[ y = 4x + 3 \] (not equivalent).

4. \( 2y - 8x = -6 \)
   Dividing by 2 gives: \[ y - 4x = -3 \] This can be rearranged to: \[ 4x - y = 3 \] (which is equivalent).

Thus, the correct response is:

\( 2y - 8x = -6 \) (This describes an infinite solution system with the original equation).