Question

Solve the system of equations using the linear combination method.

{5m+3n=41
3m−6n=9

Enter your answers in the boxes.

m =

n =

Answer 1

Do you know how to do linear combination?

Answer 2

I have been stuck on this equation and im not really good at math

Answer 3

Linear combination is basically where you have two or more equations in which you need to add them together in order to solve for a variable.

Answer 4

The first step is to setup the equations so that when you add them together, there is only on variable remaining. This requires a simple look to see where and if you need to adjust the equations. Since no variables cancel out on their own through just adding them, I need to multiply one of the equations by some factor.

\[5m+3n=41\]
\[3m−6n=9\]

It would seem the simplest way is to have 6n - 6n in order to get just have the variable m at the end. So we do:

\[2(5m + 3n = 41) \]
\[10m + 6n = 82\]

Now we add

\[10m + 6n = 82\]
With
\[3m - 6n = 9\]
We get:
\[13m = 91\]
Divide by 13
\[m = 7\]

Answer 5

Does that make sense to you?

Answer 6

Yes it does thank you

Answer 7

What do you think we do next?

Answer 8

We have to figure out what N is?

Answer 9

Correct. And how do we go about doing that?

Answer 10

How did you get 13 and 91?

Answer 11

10m + 6n = 82
3m - 6n = 9

Add these two equations together

Like terms:
10m + 3m = 13m
6n - 6n = 0
82 + 9 = 91

Answer 12

Oh I get it now

Answer 13

So do you know what we need to do next?

Answer 14

Not gonna lie im not sure

Answer 15

It is a process known as substitution. Essentially you want to substitute the value of 7 for m into one of the variables. Then there is only one unknown, n, thus you can solve for it.

Answer 16

okay and as we are talking and solving the equation im writing it down in my notes

Answer 17

What equation do you want to use?

Answer 18

@mistyrose

Answer 19

sorry i was doing something for mom

Answer 20

</3

Answer 21

I have never been smart when it came to any kind math

Answer 22

Review what we went over, them come back here.

Answer 23

Substitution:

\[3m−6n=9\]
\[3(7) - 6n = 9\]
\[21 - 6n = 9\]
Subtract 21 from both sides
\[-6n = -12\]
Divide both sides by -6
\[n = 2\]

Answer 24

okay I will and thanks for the help

Answer 25

No problem