Which equation describes an infinite solution system with the equation y=4x−3

Question

y
=
4
x
−
3
?(1 point)
Responses

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

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

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

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

Answer 1

To find an equation that describes an infinite solution system with the given equation \( y = 4x - 3 \), we need to look for an equation that represents the same line.

The equation \( y = 4x - 3 \) can be transformed into standard form. Let's rearrange it:

1. Start with \( y = 4x - 3 \).
2. Subtract \( 4x \) from both sides: \[ -4x + y = -3 \]
3. Multiply through by -1 to make the coefficients positive: \[ 4x - y = 3 \]
4. Rearranging gives: \[ 4x - y - 3 = 0 \]

Now let's check which of the provided options can be rearranged or transformed to represent the same line.

We need to check which of the provided equations can become equivalent to \( y = 4x - 3 \):

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

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

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

   Rearranging: \[ 2y = 8x - 6 \implies y = 4x - 3 \quad \text{(equivalent)} \]

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

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

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

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

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

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

This represents the same line, thus creating an infinite solution system.