Question

Given the following system of equations, identify the type of system.

y = -x + 4
2x + 2y = 8

A. inconsistent
b. equivalent

Answer 1

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

Answer 2

i dont know how. van you explain?

Answer 3

think of 2x+2y as 2y+2x

what operation will undo that +2x ?

Answer 4

subtract 2 from both sides?

Answer 5

2x actually

Answer 6

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

Answer 7

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?

Answer 8

hint: 2y means "2 times y"

Answer 9

divide 2 from both sides?

Answer 10

divide both sides by 2, yes

Answer 11

what do you get when you do this?

Answer 12

y = -2x +4?

Answer 13

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

Answer 14

y=x+4?

Answer 15

since it works like this

\[\Large 2y = -2x + 8\]

\[\Large \frac{2y}{2} = \frac{-2x + 8}{2}\]

\[\Large \frac{2y}{2} = \frac{-2x}{2} + \frac{8}{2}\]

\[\Large y = ??\]

Answer 16

x+4 is close, but no

Answer 17

x+3?

Answer 18

you had the +4 part correct

Answer 19

the "x" part was incorrect

Answer 20

why is x incorect?

Answer 21

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

Answer 22

x?

Answer 23

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

Answer 24

isnt that the same thing??

Answer 25

-x?

Answer 26

yes -x

Answer 27

so we will have

y = -x + 4

Answer 28

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

Answer 29

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

Answer 30

thank you for your help

Answer 31

another term for this is "dependent"

Answer 32

yw