Question

please help me!!!
solve each system of equations using elimination and/or substitution. express your answer as an ordered pair.
5x-2y=3
2x+7y=9

Answer 1

Ok first you have to pick an equation and start isolating either the "x" or "y" variables.

Answer 2

okay, so like...
2x=9-7y?

Answer 3

Unless you prefer to do the elimination method

Answer 4

i think i'll stick to substitution. don't wanna confuse the situation more!

Answer 5

ok so you decide to isolate the "x" so now you would divde everything by 2 on both sides

Answer 6

Since you would just get a big old decimal just leave it as a fraction

Answer 7

x=9/2 - 7/2y

Answer 8

okay......... x= 4.5-3.5

Answer 9

ohhhhhhhkkkkkkaaaaaayyyyy... wow that is a lot easier the way you put it:)

Answer 10

Actually if it end there you could use the decimals. I thought it would go on forever

Answer 11

yeh, division sucks like that:)

Answer 12

You can use either way

Answer 13

anyway now "technically" we know that x = 4.5-3.5

Answer 14

so now we would substitute all the "x" values for that small equation

Answer 15

alright so like do 5(4.5)? hold up before i continue am i doing this right???

Answer 16

yeah k think i got it...

5(4.5) - 2(3.5)=3?

Answer 17

I didn't see your post correct like that, but you have to include the entire equation cause "x" doesn't just equal that

Answer 18

"x" equals 4.5 - 3.5

Answer 19

and don't forget the "y" at the end

Answer 20

so x actually equals 4.5 - 3.5y?

Answer 21

yep

Answer 22

so rewrite the equation

Answer 23

okay-
5(4.5-3.5y) wait what about the y do i just put 3.5?

Answer 24

at the end?

Answer 25

no add the "y" that's part of x's value

Answer 26

so it would be:
5(4.5-3.5y) -2y = 3

Answer 27

k- so 5(4.5 - 3.5y) -2y = 3

22.5-17.5) - 2y=3?

Answer 28

Almost the "y" doesn't dissapear

Answer 29

k so 22.5- 17.5Y-2y=3?

Answer 30

Now we would add like terms so that we only have one y

Answer 31

so -17.5 -2y

Answer 32

-17.5y*

Answer 33

forgot the "y"

Answer 34

22.5-15.5y=3?

Answer 35

No! This is a really bad mistake in math remember that a negative plus a negative is just like adding so it would be: -19.5y

Answer 36

so.... 22.5-19.5y=3?

Answer 37

yes and now just treat it like a normal equation

Answer 38

wait but doesn't 22.5-19.5=3?

Answer 39

i mean as you can see there is definately a reason i am here so maybe i'm just dumb

Answer 40

so? our goal is to find out what the heck "y" is so we would use the opposite of the order of operations

Answer 41

so 3 - 22.5 = ?

Answer 42

-19.5y?

Answer 43

no neither of them have "y" so you can't just make another "y" magicly appear

Answer 44

well that just means it equals 19.5 correct?

Answer 45

-19.5 so now we have: -19.5y = -19.5 any ideas what to do?

Answer 46

it equals 1 cuz they're the same or something right?

Answer 47

YES a negative divide by a negative is a positive

Answer 48

so now we know that y = 1

Answer 49

But what da heck does "x" equal?

Answer 50

k so like i said 1
in the end the entire answer would be (1,1)

Answer 51

Why would you say that? have you found "x" already?

Answer 52

it equals 1 cuz they're the same or something right?

Answer 53

well that just means it equals 19.5 correct?

Answer 54

No, now what were gonna do is find "x" the way we did in the beggining

Answer 55

So pick your favorite equation

Answer 56

summer assignment... answer sheet... need to know how to show my work... all that good jazz.... so i came on here so someone could help me better understand how to do it and i completely understand now.. thank you... you are my math hero, etc.... :)

Answer 57

But you know how to do the last step right?

Answer 58

yes, don't worry thank you so so so so much;)

Answer 59

:) Just in case what you do is grab one of the equations and substitute the "y" for 1 and just solve so yes it would be (1, 1)

Answer 60

thank you very much:)