Question

need help with systems of equations
-x+2y=-4
2x-3y=8 :)need to find x and y

Answer 1

@e.mccormick

Answer 2

well lets first think about what type of method you are going to be using, there are two types, the substituion and the elimination which one do you want to choose

Answer 3

OK. This time there is no obvious relationship. So, did you want to try substitution again or elimination?

Answer 4

lets do the elimination because it is lil easier @e.mccormick

Answer 5

substitution best :)

Answer 6

OK, so do substitution, solve one of the equations for x. The top one is probably easier to do since it already has just 1x. It is a -x, but there is only one of them.

Answer 7

but I dont know how to solve it for x. I have to multiply it or divide it by a number right?, but im not sure what number

Answer 8

Order of operations in reverse.

PEMDAS

Paren ( )
Exponents
Mult and Div
Add and Sub

Well, we need to reverse these to un-do things or solve for x:

Add and Sub
Mult and Div
Exponents
Paren ( )

\(-x+2y=-4\)

So first off, we look for addtion or subtractions to move away from the x. There is the 2y being added, so you must subtract it from both sides.

Answer 9

so -x=4-2y

Answer 10

which probably gives me -x=2y

Answer 11

now divide the -x to make it +x to both sides

Answer 12

x=2y/-x ?

Answer 13

Can't just drop the 4 like that. It needed to stay.

-x=4-2y

Then divide out the invisible -1.

Answer 14

so it would be x=-4+2y

Answer 15

-x means -1x

Answer 16

isn't is way easier to do elimination??

Answer 17

now after that you replace x with the other equation

Answer 18

The number 1 likes to hide.

@somy In this case, elimination would be quicker. But someone showed her substitution earlier and messed up, so we are going back over it.

Answer 19

wait so (x=4+2y)?

Answer 20

2(-4+2y)-3y=8

Answer 21

I think I have done substitution for the whole paper so I guess I have to stick to it.

Answer 22

oh okay then @e.mccormick :)

Answer 23

Now, where it is at there, you have one variable and numbers. So it is just solve for y.

Answer 24

yes lets use the order of operations

Answer 25

so y=16??

Answer 26

hmm let me double check

Answer 27

You got a sign wrong somewhere.

Answer 28

\[2(-4+2y)-3y=8\]
\[-8+4y-3y=8\]
\[-8+y\]
\[y=16\]

Answer 29

Ah, Muzzack subbed it in with the wrong sign.

Answer 30

No. That is wrong.

Answer 31

sorrry

Answer 32

oh wait wait @Muzzack y cannot be this

Answer 33

2(−4-2y)−3y=8
−8-4y−3y=8
−8-7y=8
-7y=16
y=-16/7

Answer 34

\(-x+2y=-4 \)
\(-x=-4 - 2y\)
\(x=4 + 2y\)

So that makes for:

\(2x-3y=8\)
\(2(4 + 2y)-3y=8\)

Answer 35

i think it's better for you @tif49 to watch this and do along
http://www.youtube.com/watch?v=it3vYdV_oyc

Answer 36

Muzzack, you are still using the wrong sign....

Answer 37

i think i trust you guys more than myself watching a math video hahaha

Answer 38

lol okay then :D @tif49

Answer 39

2(4+2y)−3y=8
8+4y-3y=8
8+y=8
y=0

Answer 40

now replace 0 with the other equation

Answer 41

2x-3(0)=8

Answer 42

2x=8
x=4

Answer 43

(4,0) this is ur answer

Answer 44

am i right @e.mccormick

Answer 45

thank you so much guys for your help!!! I really couldnt have done it alone. I have a few more questions, could I tag you in my next posts so you can help me?

Answer 46

And here is what I have had typed up for a bit:

\(-x+2y=-4 \)
\(2x-3y=8\)

Elimination:

Since the top has a -1x, this is easy. Multiply by it 2, then add!
\(-x+2y=-4 \)
\(2(-x+2y)=2(-4) \)
\(-2x+4y=-8 \)

Now I add that to the other one:

\(2x-3y=8\)
\(-2x+4y=-8 \)

\(2x-2x-3y+4y=8-8 \)

\(0x+1y=0 \)

The x is now 0x, so eliminated! That is why they call it elimination. And the answer for y happens to be easy now:

\(y=0\)

If I put that in either of the original equations, I get the answer for x:

\(-x+2y=-4 \)
\(2x-3y=8\)

\(-x+0=-4 \)
\(2x-0=8\)

\(-x=-4 \)
\(2x=8\)

\(x=4 \)
\(x=4\)

OK. Now for substitution:

Again, I'll use the easy one to work to start with:

\(-x+2y=-4 \)
\(-x=-4 - 2y\)
\(x=4 + 2y\)

So, we know what x is... sort of! (if we knew y was 0 we could see the answer at this point) We take this "solved" x and substitute it into the second equation:

\(2x-3y=8\)
\(2(4 + 2y)-3y=8\)
\(8 + 4y-3y=8\)
\(y=8-8\)
\(y=0\)

From there the rest is the same.

All of this checked by a graph:
https://www.desmos.com/calculator/xnclxtxagq

\(\Huge \ddot \smile\)

Answer 47

yup now its same as my answer in elimination lol @Muzzack

Answer 48

That long post I did shows both ways, and you can use that graphing tool linked at the end to check your work. Just type in the calculations for the lines and see what they are.

Answer 49

that's super clear now @e.mccormick

Answer 50

THANKYOU guyss!

Answer 51

\[\Huge \ddot \smile\]

Answer 52

LaTeX is awesome