(please walk me through this!)
Without graphing, classify each system of equations as independent, dependent, or inconsistent. Solve independent systems by graphing.
6x - 2y = 2
2 + 6x = y

- pokiedokie

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- schrodinger

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- yolomcswagginsggg

Let's solve for x. 6x−2y=2 Step 1: Add 2y to both sides. 6x−2y+2y=2+2y 6x=2y+2 Step 2: Divide both sides by 6. 6x 6 = 2y+2 6 x= 1 3 y+ 1 3 Answer: x= 1 3 y+ 1 3

- yolomcswagginsggg

thats for the first equation.

- yolomcswagginsggg

1/3 y+ 1/3

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## More answers

- anonymous

yikes

- pokiedokie

oh.. thank you!! that was easier than i expected

- yolomcswagginsggg

lol

- anonymous

\[6x - 2y = 2 \\2 + 6x = y\] you can substitute \(2+6x\) for \(y\) in the first equation, since that is what it is
you get \[6x-2(2+6x)=2\]

- anonymous

@pokiedokie it might seem easy but that answer is totally wrong

- pokiedokie

oh whoops...

- anonymous

you are solving a system of equations, i.e. where the lines intersect.
you are not solving for x and y in one equation which is impossible

- anonymous

do you understand what i wrote above?

- pokiedokie

yes i do understand a bit of it

- anonymous

can you solve \[6x-2(2+6x)=2\] for \(x\)?

- pokiedokie

i think so, but i'm still a little confused on where to start in the equation. like as in, do i take care of the parentheses first like in PEMDAS

- anonymous

no it is not arithmetic, it is algebra
first use the distributive law to get rid of the parentheses

- pokiedokie

OH, okay thats what i meant sorry, yikes...
so i distributed, is this correct:
6x - 4 + 12x = 2

- anonymous

yes

- anonymous

now combine like terms on the left

- anonymous

oh sorry, no it is not right, but it is close

- anonymous

\[6x - 4 -12x = 2
\] is more like it

- pokiedokie

oh okay, give me a second to combine

- pokiedokie

sorry, i'm terrible at math but do you mean combining 6x with 12x or 4 and 2

- anonymous

i mean do \[6x-12x\]

- pokiedokie

im pretty sure the placement in what i put is wrong but it is
x - 4-6x = 2

- anonymous

what is \(6-12\)?

- pokiedokie

-6

- anonymous

ok so \[6x-12x=-6x\] right?

- yolomcswagginsggg

:P

- anonymous

so you should have \[-6x-4=2\] add \(4\) next

- pokiedokie

-6x = 6??

- pokiedokie

and then i just divide

- pokiedokie

@satellite73 the answer is -1, correct?

- anonymous

yes

- pokiedokie

thank you so much, sorry for being a pain in the butt!!

- anonymous

no problem
btw this makes it "consistent" the fact that you get an answer

- pokiedokie

noted, thank you very much!

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