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.