Question

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

Answer 1

To determine which equation describes a system with an infinite number of solutions, we need to find an equation that is equivalent to \( y = 4x - 3 \).

1. Start with the given equation:
\[
y = 4x - 3
\]

2. Rearranging this to the standard form gives us:
\[
-4x + y = -3
\]
or
\[
4x - y = 3
\]

3. Now we will consider the proposed equations to find which one is equivalent to the form we derived.

- **Option 1:** \( 2y - 8x = -6 \)

Divide the entire equation by 2:
\[
y - 4x = -3 \quad \text{(or rearranging, } y = 4x - 3\text{)}
\]

- **Option 2:** \( 2y - 8x = 6 \)

This can be simplified to:
\[
y - 4x = 3 \quad \text{(or } y = 4x + 3\text{, not the same)}
\]

- **Option 3:** \( 2y + 8x = -6 \)

This will lead to:
\[
y + 4x = -3 \quad \text{(or } y = -4x - 3\text{, not the same)}
\]

- **Option 4:** \( -2y + 8x = -6 \)

Rearranging gives:
\[
-2y = -6 - 8x \quad \Rightarrow \quad 2y = 8x + 6 \quad \Rightarrow \quad y = 4x + 3 \text{ (not equivalent)}
\]

From this analysis, the equation that represents a system with infinite solutions (the same line as \( y = 4x - 3 \)) is:

**2y - 8x = -6**.

Thus, the correct answer is:
**2y − 8x = −6**.