hich 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 6

−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

Answer 1

To determine which equation describes an infinite solution system with the given equation \( y = 4x - 3 \), we need to convert \( y = 4x - 3 \) into standard form and look for equivalent equations.

The given equation is: \[ y = 4x - 3 \]

Rearranging, we get: \[ 4x - y - 3 = 0 \rightarrow 4x - y = 3 \]

Now, we can form a standard linear equation: \[ 4x - y = 3 \]

Next, we need to check each of the given equations to see if they are equivalent to this.

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

   • Rearranging gives \( y = 4x + 3 \), which is not equivalent.

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

   • Rearranging gives \( 2y = 8x + 6 \) or \( y = 4x + 3 \), which is not equivalent.

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

   • Rearranging gives \( 2y = -8x - 6 \) or \( y = -4x - 3 \), which is not equivalent.

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

   • Rearranging gives \( 2y = 8x - 6 \) or \( y = 4x - 3 \), which is equivalent!

Thus, the equation that describes an infinite solution system is: \[ \boxed{2y - 8x = -6} \]