Question

Solve the system of equations algebraically. (Fractions)
M/4 - N/4 =1
M/6 - N/4 =1

Answer 1

subtract the bottom equation from the top to solve for M. plug M into the second equation to solve for N.

Answer 2

another way to do it, which I'm still a little iffy about it, but by all means its there @nsutton would this work?

tweak with the equation, the first one lets say:

m/4-n/4=1
=
m/4=1+n/4
=
m=4+n

and then in the next equation plug in for m

(4+n)/6 - n/4 = 1

and then just solve for n which later will give you m

Answer 3

M/4 - N/4 =1, M/6 - N/4 =1
(M-N)=4, 2M-3N=2
M=4+N, 2(4+N)-3N=2 SOLVE THE TWO EQUATIONS

Answer 4

@rits27 on your second line second equation did you mean 12 also on the third line.. seems to me you multiplied everything by 12

Answer 5

also, since m/4-n/4=1 and m/6-n/4=1 you can say that they are both equal to each other and thus:

m/4-n/4=m/6-n/4

and then you can combine like terms and still get what I sated above

Answer 6

Yes you take a factors of 6 and 4
and then multiply both sides by it

Answer 7

so for the first equation you divide by 4?

Answer 8

first equation you multiply by 4 both sides

Answer 9

to solve for M? (M/4 - 4/N = 1) becomes M-N =4

Answer 10

what was done there was that it was tweaked, whatever you do to the right, you do the the left. in this case you want to isolate the M so you add N to both sides

Answer 11

Yes

Answer 12

so it becomes M = N+4?

Answer 13

Now substitute the value of M i.e. N+4 in the other equation

Answer 14

Does the second equation need to be multiplied also?

Answer 15

@seattle12345 not if you have multiplied one already. multiplying in this case allows you to work without fractions. So I guess it depends. If you want to work with fractions or not. Which working without them does make it simpler usually..

Answer 16

yea I would choose not to work with fractions. so in the second equation we end up with 2M -3N = 2... How did we end up with the 2(constant) if we multiplied by 12? sorry if its a stupid question.

Answer 17

12M/6 is 2M

Answer 18

and 12*N/4 is 3N

Answer 19

sorry I mean the (=2)

Answer 20

Its not 2 its 12 actually

Answer 21

oh ok, it makes more sense now lol

Answer 22

so N=4?

Answer 23

N= -4?

Answer 24

2(4+N)-3N=12
ie 8+2N-3N=12
ie -N=12-8
ie N=-4.

Answer 25

Thanks for your help @rits27 @nsutton and @juan_9292! you guys are amazing!