To find which equation describes an infinite solution system with the equation \( y = 4x - 3 \), we need to look for an equation that is equivalent to this one.
An equation has infinite solutions if it is just a multiple of the given equation.
Starting with the given equation:
\[ y = 4x - 3 \]
Now let's rewrite this equation in standard form \( Ax + By + C = 0 \):
- Move all terms to one side: \[ -4x + y + 3 = 0 \] or \[ 4x - y - 3 = 0 \]
Now, let's analyze each of the answer choices to see if they are equivalent to this equation:
A. \( 2y + 8x = -6 \)
- Rearranging gives: \( 2y = -8x - 6 \) or \( y = -4x - 3 \) (not equivalent)
B. \( 2y - 8x = 6 \)
- Rearranging gives: \( 2y = 8x + 6 \) or \( y = 4x + 3 \) (not equivalent)
C. \( -2y + 8x = -6 \)
- Rearranging gives: \( -2y = -8x - 6 \) or \( y = 4x + 3 \) (not equivalent)
D. \( 2y - 8x = -6 \)
- Rearranging gives: \( 2y = 8x - 6 \) or \( y = 4x - 3 \)
The equation in choice D is equivalent to the original equation \( y = 4x - 3 \).
So the answer is:
D. \( 2y - 8x = -6 \)
1 answer