Question

Which equation describes an infinite solution system with the equation y=4x−3 ?(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 identify which equation describes an infinite solution system with the equation \( y = 4x - 3 \), we need to find an equivalent equation.

An equivalent equation will have the same slope and y-intercept.

Starting with \( y = 4x - 3 \), we can rearrange it into the standard form \( Ax + By = C \):

1. **Starting equation**:
\[ y = 4x - 3 \]

2. **Rearranging**:
\[ -4x + y = -3 \]
or equivalently
\[ 4x - y = 3 \]

Now we need to check each of the options provided to see if they can be rearranged to match this form.

1. **Option 1**: \( -2y + 8x = -6 \)
- Rearranging gives \( 2y = 8x + 6 \) or \( y = 4x + 3 \) (not equivalent).

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

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

4. **Option 4**: \( 2y - 8x = -6 \)
- Rearranging gives \( 2y = 8x - 6 \) or \( y = 4x - 3 \) (equivalent).

The equation that describes an infinite solution system with \( y = 4x - 3 \) is:
**2y - 8x = -6**.