Question

Please help me on my Solving Systems of Linear Equations homework!

Answer 1

\[\frac{ 4a }{ d }x-\frac{ c }{ 5d }y=\frac{ m }{ d }\]
\[2ax+\frac{ c }{ 5 }y=n\]

Answer 2

solving for what ?

Answer 3

for x and y ?

Answer 4

Yes

Answer 5

what will be the common denominator in case the first equation ?

Answer 6

please collaborate - i like help you step by step

Answer 7

d

Answer 8

not d bc. there is 5d

Answer 9

1?

Answer 10

when there are d and 5d denominators so what will be the common denominator ?

Answer 11

I think I would first multiply the first equation (both sides, all terms) by "d"

Answer 12

5?

Answer 13

this is one good idea this above wrote by @phi

Answer 14

But what about the 5?

Answer 15

we will get to that. But first, what do you get if you multiply the first equation by "d" ?
can you do that ?

Answer 16

4ax-y(c/5)=m

Answer 17

yes. we got rid of (most) of the fractions
now notice the (new) top equation has -y(c/5)
and the bottom equation has +y(c/5)
what happens when we add the two equations? Do you see y(c/5) - y(c/5) = 0

Answer 18

do you know how to add
4ax-y(c/5)=m
2ax+y(c/5)= n

?

Answer 19

Is it 2ax+4ax=m+n or 6ax=m+n?

Answer 20

yes

Answer 21

Then do I divide m+n by 6a?

Answer 22

yes, you get
\[ x = \frac{m+n}{6a} \]

Answer 23

Do I plug that in a solve for y then?

Answer 24

It's very big

Answer 25

I would use the 2nd equation (it looks a bit simpler)
you get
\[ 2a \cdot \frac{m+n}{6a} +\frac{c}{5}y= n \]

Answer 26

Can it be simplified into m+n/3a?

Answer 27

the first term? notice a/a simplifies to 1 and 2/6 to 1/3

Answer 28

So is it m+n/3?

Answer 29

yes, you get
\[ \frac{m+n}{3} +\frac{c}{5}y= n\]
I would subtract (m+n)/3 from both sides

Answer 30

(c/5)y=n-(m+n/3)

Answer 31

and it might look a bit nicer if you write n as 3n/3 and simplify the right side

Answer 32

(c/5)y=m+n?

Answer 33

\[ \frac{c}{5} y = \frac{3n}{3} - \frac{m+n}{3} \]

Answer 34

(c/5)y=2n-m?

Answer 35

\[ \frac{c}{5} y = \frac{3n- m-n}{3} \]

Answer 36

you seem to be missing the denominator (the 3)

Answer 37

Oh,

(c/5)y=2n-m/3

Answer 38

yes, and it's better to put in the parens:
(c/5)y= (2n-m)/3


the last step is multiply both sides by 5/c

Answer 39

y=(10n-5m)/3c

Answer 40

yes. I would leave it as
\[ y= \frac{5(2n-m)}{3c} \]
(but your way is ok. )

Answer 41

Thank you so much!!

Answer 42

So x is (m+n)/6a and y is 5(2n-m)/3c?

Answer 43

yes

Answer 44

Thank you so much then!!