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

Step-by-step explanation:

Given

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 has m has its slope.

In

--- slope

Considering the options

Make y the subject

Divide by 3

The slope is:

Hence, (a) can make a consistent and independent system with

The slope is:

Hence, (b) can make a consistent and independent system with

The slope is:

Hence, (c) cannot make a consistent and independent system with

Make y the subject

Divide by 2

The slope is

Hence, (d) cannot make a consistent and independent system with

Make y the subject

Divide by 3

The slope is:

Hence, (e) can make a consistent and independent system with

x = -5

step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.