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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

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 class=

Respuesta :

calculista

Answer:

x=3y-2

y=-3x-2

3y-x=-2

Step-by-step explanation:

we know that

To create a consistent and independent system, the slope of the other equation must be different at the slope of the given equation.

A consistent and independent system has only one solution

we have

y=3x-2

The slope of the given equation is m=3

so

Verify the slope of each case

case 1) we have

x=3y-2

isolate the variable y

3y=x+2 ------> y=(1/3)x+(2/3)

The slope is m=1/3

therefore

This equation can pair with the given equation to create a consistent and independent system, because their slopes are different

case 2) we have

y=-3x-2

The slope is m=-3

therefore

This equation can pair with the given equation to create a consistent and independent system, because their slopes are different

case 3) we have

y=3x+2

The slope is m=3

Parallel lines with different y-intercepts (The system has no solution)

therefore

This equation cannot pair with the given equation to create a consistent and independent system, because their slopes are the same

case 4) we have

6x-2y=4

isolate the variable y

2y=6x-4

y=3x-2

The slope is m=3

Is the same given equation (is a consistent and dependent system, has infinitely solutions)

therefore

This equation cannot pair with the given equation to create a consistent and independent system, because their slopes are the same

case 5) we have

3y-x=-2

isolate the variable y

3y=x-2

y=(1/3)x-(2/3)

The slope is m=1/3

therefore

This equation can pair with the given equation to create a consistent and independent system, because their slopes are different

abidemiokin

The equations that can pair with y = 3x – 2 to create a consistent and independent system are x = 3y - 2, y = -3x - 2 and 3y -x = -2

In order to get an equation that  creates a consistent and independent system, the slope of the given line must differ from the required line

The standard form of the equation of a line is expressed as y = mx + b

m is the slope of the line

Given the equation y = 3x - 2

Compared with the general equation;

mx = 3x

m = 3

Hence we must find an equation that has an equation with a slope not 3

From the given option

x = 3y – 2

3y = x + 2

y = 1/3 x + 2

The slope is 1/3, hence the equation fits the required. Same with the equation y = -3x -2 with a slope of -3 .

For the equation 3y - x = -2

3y = x - 2

y = 1/3 x - 2

This equation is also correct.

Hence the equations that can pair with y = 3x – 2 to create a consistent and independent system are x = 3y - 2, y = -3x - 2 and 3y -x = -2

Learn more here; https://brainly.com/question/16949303

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