Question

Which equation describes an infinite solution system with the equation: y = 4x - 3
A. -2y + 8x = -6
B. 2y - 8x = -6
C. 2y - 8x = 6
D. 2y + 8x = -6

Answer 1

To determine which equation describes an infinite solution system with the equation \( y = 4x - 3 \), we need to find an equation that is equivalent to it.

The given equation is in slope-intercept form ( \( y = mx + b \) ), where \( m = 4 \) and \( b = -3 \).

To compare, let's rewrite the given equation in standard form (Ax + By = C) and check each option.

Starting with \( y = 4x - 3 \):

1. Rearranging gives:
\[
-4x + y = -3
\]
or,
\[
4x - y = 3
\]

Now, we will check each option to see if it represents the same line.

A. \(-2y + 8x = -6\)

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

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

Rearranging gives:
\[
2y = 8x - 6
\]
\[
y = 4x - 3 \quad \text{(equivalent, therefore infinite solutions)}
\]

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

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

D. \(2y + 8x = -6\)

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

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

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

This system has infinite solutions.