Solution Sets of Simultaneous Equations Quick Check

Question

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

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

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

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

2y−8x=6

Answer 1

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 equation.

The given equation can be rearranged to find the same line in different forms.

Starting from \( y = 4x - 3 \), we can multiply the entire equation by 2 to get:

\[ 2y = 8x - 6 \]

Rearranging this gives:

\[ 2y - 8x = -6 \]

Now let's look at the provided options:

1. \( -2y + 8x = -6 \) (Not equivalent)
2. \( 2y - 8x = -6 \) (Equivalent)
3. \( 2y + 8x = -6 \) (Not equivalent)
4. \( 2y - 8x = 6 \) (Not equivalent)

The equation that describes an infinite solution system with the equation \( y = 4x - 3 \) is:

2y − 8x = −6.