Question

Which equation describes an infinite solution system with the equation y=4x−3 ?(1 point) Responses 2y+8x=−6 2 y plus 8 x equals negative 6 2y−8x=−6 2 y minus 8 x equals negative 6 2y−8x=6 2 y minus 8 x equals 6 −2y+8x=−6

Answer 1

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

The original equation can be rewritten in standard form:

1. Start with \( y = 4x - 3 \).
2. Rearranging gives: \( -4x + y = -3 \).
3. To make it into a more standard form, multiply by -1: \( 4x - y = 3 \).

Now, we can multiply this equation by 2, since any multiple of an equivalent equation will represent the same line:

\[
2(4x - y) = 2(3) \Rightarrow 8x - 2y = 6
\]

This is not one of your options, but we can manipulate the forms of the options provided to see if they are equivalent. Let's check each option:

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

The only option that is equivalent to \( y = 4x - 3 \) is:

**\( 2y - 8x = -6\)**.

This option represents an infinite solution system with the given equation.