3. 3x-4y=5

6x-8y=-5

3. 3x-4y=5

6x-8y=-5

Tutors, sign in to answer this question.

Kara,

There are many ways to solve this problem. I'm assuming your okay with the definition of independent, dependent and inconsistent systems of equations (let me know if my assumption is incorrect), and that you can easily recognize slope and y-intercepts for a line (I'll be glad to review this if it is needed).

The easiest way to see that this is an inconsistent system is to note that the lines have the same slope, but a different y intercept. That means that they will start at different points (different y-intercept) and then increase at the same rate (same slope). The result is that they will never meet.

Meagan W. | Biology, Mathematics and Statistics TutoringBiology, Mathematics and Statistics Tuto...

First we want to solve for "y"

EQ1:

3x-4y = 5

4y = 3x-5

y = (3x-5)/4

EQ2:

6x-8y = 5

8y = 6x-5

y = (6x-5)/8

Recall the definitions:

A set of equations is consistent and independent if they have only one intersection.

A set of equations is consistent and dependent if they are the same line.

A set of equations is inconsistent if they do not have a point of intersection.

Now we want to see if there are any points of intersection. Set the equations equal to eachother and solve for x:

(3x-5)/4 = (6x-5)/8

2*(3x-5) = (6x-5)

6x-10 = 6x-5

-10 = -5

So, we do not have any points of intersection. This means that the equations are inconsistent.

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Michael B.

Effective Tutor Specializing in Mathematics

$10 per 15 min

View Profile >

Rebecca D.

Experienced and Patient Tutor for Math and Reading

$10.75 per 15 min

View Profile >

Randee S.

Dynamic, versatile tutor for core subject areas K-12

$8.75 per 15 min

View Profile >