- anonymous

Given the following system of equations, identify the type of system.
y = -x + 4
2x + 2y = 8
A. inconsistent
b. equivalent

- jamiebookeater

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- jim_thompson5910

are you able to solve 2x + 2y = 8 for y?

- anonymous

i dont know how. van you explain?

- jim_thompson5910

think of 2x+2y as 2y+2x
what operation will undo that +2x ?

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## More answers

- anonymous

subtract 2 from both sides?

- jim_thompson5910

2x actually

- jim_thompson5910

so we will have 2y = 8 - 2x which is the same as 2y = -2x + 8

- jim_thompson5910

we want to isolate y fully
so we have to move that 2 (from 2y) over to the other side. How do we do this?

- jim_thompson5910

hint: 2y means "2 times y"

- anonymous

divide 2 from both sides?

- jim_thompson5910

divide both sides by 2, yes

- jim_thompson5910

what do you get when you do this?

- anonymous

y = -2x +4?

- jim_thompson5910

you have to divide EVERY term by 2, not just the 8

- anonymous

y=x+4?

- jim_thompson5910

since it works like this
\[\Large 2y = -2x + 8\]
\[\Large \frac{2y}{2} = \frac{-2x + 8}{2}\]
\[\Large \frac{2y}{2} = \frac{-2x}{2} + \frac{8}{2}\]
\[\Large y = ??\]

- jim_thompson5910

x+4 is close, but no

- anonymous

x+3?

- jim_thompson5910

you had the +4 part correct

- jim_thompson5910

the "x" part was incorrect

- anonymous

why is x incorect?

- jim_thompson5910

you should divide -2x by 2 to get ????

- anonymous

x?

- jim_thompson5910

nope not x, you are thinking of 2x divided by 2

- anonymous

isnt that the same thing??

- anonymous

-x?

- jim_thompson5910

yes -x

- jim_thompson5910

so we will have
y = -x + 4

- jim_thompson5910

2x + 2y = 8 turns into y = -x + 4 when you solve for y

- jim_thompson5910

so y = -x + 4 and 2x + 2y = 8 are equivalent (ie the same exact equations)

- anonymous

thank you for your help

- jim_thompson5910

another term for this is "dependent"

- jim_thompson5910

yw

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