Please help with the following problem. 3m-6n=12 4m-8n=16Is this problem dependent or inconsistent?

3 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve for m and n given the system of equations:

3m - 6n = 12 ...(1)

4m - 8n = 16 ...(2)

If both the sides of (1) are divided by 3, we get m - 2n = 4

Again, if both the sides of (2) are divided by 4, we get m - 2n = 4

The two equations are not independent. This does not allow us to obtain unique values of m and n. We can only say that for any value of m or n they are related as m = 4 + 2n

The equations are dependent and cannot be solved for unique solutions of m and n.

samhouston's profile pic

samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted on

This is a system of linear equations.

3m-6n=12

4m-8n=16

You need to first eliminate one of the variables by giving them equal but opposite coefficients.  Multiply the first equation by -4 and the second equation by 3.

-4(3m-6n=12)

3(4m-8n=16)

After you have done this, the new system is...

-12m + 24n = -48

12m - 24n = 48

Now add the systems.

The solution is 0 = 0.

Since this is always true, the system in consistent.  The lines are coincident, meaning that they lay on top of each other.

iislas104's profile pic

iislas104 | High School Teacher | (Level 1) eNoter

Posted on

If you are allowed to solve using a graphing calculator I think that is the easiest way to find the answer. If you are not allowed to use the calculator it is still pretty easy to solve it just takes a lot more steps.  I would graph the two equations and see if they intersect. (I am going to asume you already know how to graph these equations okay) WHen you graph the 2 equations if they intersect at one point then they have one solution and are consistent and independent, if they  are parallel lines when you graph them then they have NO solution and are inconsistent, and finally if they are the same line (one line ontop of the other) then they have infinitely many solutions and they are consistent and dependent. I did not give you the exact answer but i have given you all the info you need to find the exact answer. Let me know if you need more help.

We’ve answered 318,957 questions. We can answer yours, too.

Ask a question