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

Answer 1

Answer:

$(a)\ x = 3y - 2$

$(b)\ y = -3x - 2$

$(e)\ 3y - x = -2$

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 $y =3x -2$