Question

Solve the following system and show all of your work.
x − 2y = 14
x + 3y = 9

Answer 1

SOMEONE.

Answer 2

sorry ^-^!!!

Answer 3

I think u got it though.

Answer 4

uhh.. you erased it.. I dont know what it is. haha

Answer 5

Oh well. cya!

Answer 6

multiply the bottom equation by -1
that means multiply -1 times each term on both sides
can you do that ?

Answer 7

is this for hw or a quiz/test?

Answer 8

this is homework.

Answer 9

but @phi why -1? where am i getting that?

Answer 10

(3x+2)(x+4) don't listen to him he's wrong.

Answer 11

foil --> 3x^2+12x+2x+8 --> 3x^2+14x+8

Answer 12

you will see in a minute. we are going to make the x term go away

Answer 13

see, it's the original answer.

Answer 14

this is a method I've never seen of before ^^^^^^ from phi

Answer 15

@daren13354 please do not spam

Answer 16

multiply the bottom equation by -1
that means multiply -1 times each term on both sides
can you do that ?

Answer 17

then add the 2 equations together.

Answer 18

no this is for substitution. not elimination.

Answer 19

ok. (but in the long run, elimination seems easier).
but to do substitution on these
x − 2y = 14
x + 3y = 9

pick one of the variables to isolate. in this case x looks easier.
if we use the first equation: write +2y on both sides of the equal sign and then simplify

Answer 20

ok so i have x=14+2y

Answer 21

now in the 2nd equation
x+3y= 9
replace the x with its equivalent value 14+2y
simplify

Answer 22

where do i start first? Combine like terms? subtract 14?

Answer 23

what do you have for an equation?

Answer 24

14+2y+3y=9

Answer 25

ok. order does not matter when simplifying. But I would combine the y terms, and also add -14 to both sides of the equation.

Answer 26

i got y= -1

Answer 27

now pick one of the original equations, and replace "y" with -1. simplify to find what x is

Answer 28

or use
x=14+2y
which you found. already to plug in y= -1 to find x

Answer 29

so... orignal: x-2y=14
now: x-2-1=14

Answer 30

??

Answer 31

x-2y=14

remember -2y is short hand (because people are lazy and don't like to type)
-2y is short for -2*y (-2 times y)

Answer 32

wait...how do i start to solve for x

Answer 33

you have
x- 2*y= 14
replace y with -1
what do you get?

Answer 34

like i said up there. x-2y(-1)=14

Answer 35

correct?

Answer 36

replace y. so where you see y, write -1 in
x - 2*y=14

Answer 37

ok now what

Answer 38

what do you have for an equation?

Answer 39

just what do i do now. i have -1 in for y. whats next

Answer 40

multiply the 2 numbers. then solve for x

Answer 41

i got x=16

Answer 42

........

Answer 43

write down the equation you started with, and let's see where you went wrong.

Answer 44

x-2(-1)=14

Answer 45

I am thinking when you started with
x - 2* -1 =14
you should

think of this as x + -2*-1=14 so when you multiply -2*-1 you get +2

or you could do
x - 2*(-1)=14 and 2*-1 is -2:
x - -2 = 14
and minus a minus is plus:
x + 2=14

does that make sense?

Answer 46

now add -2 to both sides to get x

Answer 47

or, remember up top where you found
"ok so i have x=14+2y"

you could replace y with -1 in this equation:
x= 14+ 2*-1
2*-1 is -2 so you get
x= 14-2
x=12

maybe that is the easiest way.