Question

..

Answer 1

@priyar Lend a quick hand?!

Answer 2

y not normally by substitution ?

Answer 3

Thats what they are asking for in my book

Answer 4

but the Q says.."Solve this system by substitution."

Answer 5

okay then just do substitution..as u do usually

Answer 6

Yes, Im saying thats what they want. Substitution. Im better at elimination.

Answer 7

find r from first eq and substitute in the second..

Answer 8

Take me through the steps of substitution for this problem if you don't mind? I think I have an idea of how to do it, but I can't afford to get this wrong.

Answer 9

take the first equation
\[r+s=-12\]solve it for \(r\) in terms of \(s\), what do you get?

Answer 10

subtract s on both sides..in first eq so that u have only r on the left side..

Answer 11

ok ill show you what I have so far, then just pick up after me..

Answer 12

this is the first step for any substitution problem..(u must have only 1 variable on left side...)

Answer 13

r+s=-12
r+s-s=-12-s
r=-12-s

Answer 14

good. now in the second equation\[4r-6s=12\]replace \(r\) everywhere with \((-12-s)\)

Answer 15

that gives you an equation just in terms of \(r\) which you should be able to easily solve.

Answer 16

so we are making the second eq. to have just "one variable"

Answer 17

then just find \(s\) from your value for \(r\) using your substitution equation\[r=-12-s\]

Answer 18

sorry! I switched the names. you solve for \(s\) then get the value of \(r\)

Answer 19

its like "erasing " r and writing -12-s in its place

Answer 20

so what do u get?

Answer 21

4r-6s=12
4r-6s-4r=12-4r
6s=12-4r

is that correct? for the second equation?

Answer 22

u didn't replace r with "-12-s"..in the second eq..

Answer 23

I thought we had to do it like I did above before I substituted

Answer 24

ok..@LetsLearn2000 but still u hav emade a mistake in sign..

Answer 25

Why'd you delete your comment? @whpalmer4

Answer 26

its -6s=12-4r ok?

Answer 27

4r-6s=12
4r-6s-4r=12-4r
6s=12-4r

yeah thats what I did but you guys are saying I made a mistake

Answer 28

how did -6s become 6s??

Answer 29

u have made a mistake in last step..

Answer 30

I had a typo in it

\[r+s=-12\]\[r=-12-s\]that is the substitution equation

second equation is \[4r-6s=12\]replace \(r\) with \((-12-s)\) to get\[4(-12-s)-6s=12\]
simplify and solve for value of \(s\)

Answer 31

@LetsLearn2000 did u understand wht was ur mistake..?

Answer 32

Yes @priyar Im about to solve @whpalmer4

Answer 33

ok then proceed!

Answer 34

I got -2 ? @whpalmer4

Answer 35

can you show me the steps?

Answer 36

Can I just tell you what I did? I wrote it on a piece of paper and it'll take forever to type

Answer 37

well, OK, you made a mistake somewhere, just hoping to find it

Answer 38

did u proceed in ur way or whpalmer4's?

Answer 39

so that i can trace ur steps..

Answer 40

Im totally confused now.. Whichever way is the substitution way lol I believe thats @whpalmer4 's way

Answer 41

\[4(-12-s)-6s=12\]\[4(-12)+4(-s)-6s=12\]\[-48-4s-6s=12\]agree, disagree?

Answer 42

Here. I just simplified on a calc so You can see the steps instead of me typing

Answer 43

but you used wrong formula. \[r=-12-s\]NOT\[r=-12-6s\]

Answer 44

I made same typo earlier, and deleted post containing it...

Answer 45

ya..exactly..

Answer 46

Ok I see, its -6 now correct?

Answer 47

yes!

Answer 48

yes. so value of other variable is what?

Answer 49

-6 lol

Answer 50

right. and that's the same answer you would get from elimination, of course

Answer 51

\[r+s=-12\]\[4r-6s=12\]multiply first eq. by \(6\)
\[6r+6s=-72\]\[4r-6s=12\]add together to get\[6r+4r +6s-6s=-72+12\]\[10r=-60\]etc.

Answer 52

important step for either substitution or elimination: plug answers back into both equations and verify they both work!

Answer 53

ok, Thanks I appreciate it!

Answer 54

easy to come up with values that satisfy one equation but not the other. for example, you had \(s=-2\) earlier, and that would give you \(r=-10\) as other half of solution.

\[r+s=-12\]\[(-10)+(-2)=-12\]\[-12=-12\]looks good so far, right?

\[4r-6s=12\]\[4(-10)-6(-2)=12\]\[-40+12=12\]\[-28=12\]uh, nope...

Answer 55

anyhow, you can solve with either approach, useful to know both as one is often a bit easier than the other.

Answer 56

Yes. thanks once again, I may be back on in a bit, you'll be on?

Answer 57

if you tag me on a question, I will have a look when able. if someone else helps you first, I will check it and add any further points I think useful.