Question

Question

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

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

−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 minus 8 x equals 6
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Answer 1

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

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

1. Start from \( y = 4x - 3 \).
2. Rearranging gives: \( -4x + y = -3 \).
3. Multiplying by -1 to switch signs: \( 4x - y = 3 \).

Now, let's check each option to see if one of them can be rearranged to match \( 4x - y = 3 \):

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

   • Rearranging gives: \( 2y = -8x - 6 \) → \( y = -4x - 3 \) (not equivalent)

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

   • Rearranging gives: \( -2y = -8x - 6 \) → \( 2y = 8x + 6 \) → \( y = 4x + 3 \) (not equivalent)

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

   • Rearranging gives: \( 2y = 8x - 6 \) → \( y = 4x - 3 \) (equivalent)

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

   • Rearranging gives: \( 2y = 8x + 6 \) → \( y = 4x + 3 \) (not equivalent)

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

2y − 8x = −6.