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