## Which equations can pair with y = 3x – 2 to create a consistent and independent system? x = 3y – 2 y = –3x – 2 y = 3x + 2 6x – 2y = 4 3y – x

Question

Which equations can pair with y = 3x – 2 to create a consistent and independent system? x = 3y – 2 y = –3x – 2 y = 3x + 2 6x – 2y = 4 3y – x = –2

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1 year 2021-09-03T17:00:02+00:00 1 Answers 103 views 0

$$(a)\ x = 3y – 2$$

$$(b)\ y = -3x – 2$$

$$(e)\ 3y – x = -2$$

Step-by-step explanation:

Given

$$y =3x -2$$

Required

Equations that can create consistent and independent systems

For a pair of equation to have consistent and independent systems, the equations must have different slopes.

An equation of the form $$y = mx + c$$ has m has its slope.

In $$y =3x -2$$

$$m = 3$$ — slope

Considering the options

$$(a)\ x = 3y – 2$$

Make y the subject

$$x = 3y – 2$$

$$3y = x+2$$

Divide by 3

$$y = \frac{1}{3}x+\frac{2}{3}$$

The slope is:

$$m_1 = \frac{1}{3}$$

Hence, (a) can make a consistent and independent system with $$y =3x -2$$

$$(b)\ y = -3x – 2$$

The slope is:

$$m= -3$$

Hence, (b) can make a consistent and independent system with $$y =3x -2$$

$$(c)\ y = 3x + 2$$

The slope is:

$$m=3$$

Hence, (c) cannot make a consistent and independent system with $$y =3x -2$$

$$(d)\ 6x – 2y = 4$$

Make y the subject

$$2y = 6x -4$$

Divide by 2

$$y = 3x -2$$

The slope is

$$m =3$$

Hence, (d) cannot make a consistent and independent system with $$y =3x -2$$

$$(e)\ 3y – x = -2$$

Make y the subject

$$3y = x -2$$

Divide by 3

$$y = \frac{1}{3}x -\frac{2}{3}$$

The slope is:

$$m = \frac{1}{3}$$

Hence, (e) can make a consistent and independent system with $$y =3x -2$$