Question

Which equation describes an infinite solution system with the equation y=4x−3
𝑦
=
4
𝑥
−
3
?(1 point)
Responses

2y−8x=6
2
𝑦
−
8
𝑥
=
6
2 y minus 8 x equals 6

−2y+8x=−6
−
2
𝑦
+
8
𝑥
=
−
6
negative 2 y plus 8 x equals negative 6

2y+8x=−6
2
𝑦
+
8
𝑥
=
−
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 equation \( y = 4x - 3 \), we need to recognize that two equations must represent the same line in order to have infinitely many solutions.

The given equation \( y = 4x - 3 \) can be rewritten in standard form (Ax + By = C) as follows:

1. Rewrite: \( y - 4x = -3 \)
2. Rearranging gives us: \( 4x - y = 3 \)

Now, let's analyze each of the given options to check if any of them can be simplified to \( 4x - y = 3 \):

1. **\( 2y - 8x = 6 \)**:
- Dividing the entire equation by 2 gives: \( y - 4x = 3 \) or \( 4x - y = -3 \). (Not equivalent)

2. **\( -2y + 8x = -6 \)**:
- Dividing the entire equation by -2 gives: \( y - 4x = 3 \) or \( 4x - y = -3 \). (Not equivalent)

3. **\( 2y + 8x = -6 \)**:
- Dividing the entire equation by 2 gives: \( y + 4x = -3 \). (Not equivalent)

4. **\( 2y - 8x = -6 \)**:
- Dividing the entire equation by 2 gives: \( y - 4x = -3 \) or \( 4x - y = 3 \). (This is equivalent to the original equation)

From this analysis, we can conclude that the equation that describes an infinite solution system with \( y = 4x - 3 \) is:

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