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

Question

?(1 point)
Responses

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

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

2y−8x=6
2 y minus 8 x equals 6

2y−8x=−6

Answer 1

To find which equation describes an infinite solution system with the equation \( y = 4x - 3 \), we need to determine which of the given equations represents the same line as \( y = 4x - 3 \).

1. Start with the original equation: \[ y = 4x - 3 \]

2. Let's rearrange it to standard form (Ax + By = C): \[ 4x - y = 3 \] \[ -4x + y = -3 \] (We can multiply through by -1 to keep the coefficients positive)

Now let's analyze the options:

1. Option 1: \( -2y + 8x = -6 \) Rearranging gives: \[ -2y = -8x - 6 \] \[ y = 4x + 3 \] (not the same line)

2. Option 2: \( 2y + 8x = -6 \) Rearranging gives: \[ 2y = -8x - 6 \] \[ y = -4x - 3 \] (not the same line)

3. Option 3: \( 2y - 8x = 6 \) Rearranging gives: \[ 2y = 8x + 6 \] \[ y = 4x + 3 \] (not the same line)

4. Option 4: \( 2y - 8x = -6 \) Rearranging gives: \[ 2y = 8x - 6 \] \[ y = 4x - 3 \] (this is the same line)

The correct response that describes an infinite solution system with the equation \( y = 4x - 3 \) is:

2y - 8x = -6.