Question

Solve the system using linear combinations.

3m + 2n = 10

4m – n = –1
I need someone to tell me if im doing this right im not sure if I get this or not =/

Answer 1

ok so I should start by multiplying right?

Answer 2

yep \(\rm\color{green}{o^\wedge\_^\wedge o}\)

Answer 3

\[-4(3m+2n=10)\]
\[3(4m – n = –1)\]

Answer 4

that works but I think you took the harder route

Answer 5

you can do matrix 9just set it up and solve), substitution (rearrange the second equation), or elimination (multiply the equation to make the values of one of variables be additive inverses in the 2 equations)

Answer 6

=/ im confused xD and i realize i dont get this :(

Answer 7

you could did what you did... (or what I thought was easier which was to multiply the second equation by 2 then add the equations together )
But your way works as well. You just have to multiply both equations be a number which is not too much extra work.

Answer 8

distribute your -4 to your first equation and your 3 to your second
then add your equations

Answer 9

\(\large\color{slate}{ 3m + 2n = 10 }\)
\(\large\color{slate}{ 4m - n = -1 }\) >>> \(\large\color{slate}{ 4m +1 = n }\)

\(\large\color{slate}{ 3m + 2(4m +1 ) = 10 }\)

Answer 10

not so hard:P

Answer 11

then solve for n as you find M

Answer 12

I see a sub as the quickest approach

Answer 13

you have to multiply by something so you can cancel out one variable
first equation have positive 2n so you can multiply 2nd equation by just 2
\(\rm\color{green}{o^\wedge\_^\wedge o}\) \(\rm\color{green}{o^\wedge\_^\wedge o}\)

Answer 14

\[3m+8m+2=10\]

Answer 15

and then 11m+2=10
11m=7??????

Answer 16

10-2 is 8 (not 7)
yes, apparently m=11/8

Answer 17

I mean m=8/11

Answer 18

oops sorry right and then now i would just plug that into one of the equations right?

Answer 19

yes, I would plug m=8/11 into both of the equations to also verify it

Answer 20

https://www.desmos.com/calculator/pvyxhl5bzg
verification

Answer 21

Oh ok thanks i got it :D

Answer 22

:)