Which equation describes an infinite solution system with the equation y=4x−3 ?(1 point)

Question

Responses

2y−8x=−6
2 y minus 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 determine which equation describes an infinite solution system with the equation \( y = 4x - 3 \), we need to find an equation that is essentially equivalent to it. This means we will want an equation that can be transformed into \( y = 4x - 3 \) through algebraic manipulation.

Let’s analyze each option:

1. Option 1: \( 2y - 8x = -6 \)

   Rearranging this: \[ 2y = 8x - 6 \ y = 4x - 3 \] This is equivalent to the original equation \( y = 4x - 3 \).

2. Option 2: \( 2y + 8x = -6 \)

   Rearranging this: \[ 2y = -8x - 6 \ y = -4x - 3 \] This is not equivalent to the original equation.

3. Option 3: \( 2y - 8x = 6 \)

   Rearranging this: \[ 2y = 8x + 6 \ y = 4x + 3 \] This is also not equivalent to the original equation.

4. Option 4: \( -2y + 8x = -6 \)

   Rearranging this: \[ -2y = -8x - 6 \ 2y = 8x + 6 \ y = 4x + 3 \] This is also not equivalent to the original equation.

Therefore, the only equation that is equivalent to \( y = 4x - 3 \) is Option 1: \( 2y - 8x = -6 \), which describes an infinite solution system with the given equation.