anonymous
  • anonymous
Given the following system of equations, identify the type of system. y = -x + 4 2x + 2y = 8 A. inconsistent b. equivalent
Mathematics
jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
are you able to solve 2x + 2y = 8 for y?
anonymous
  • anonymous
i dont know how. van you explain?
jim_thompson5910
  • jim_thompson5910
think of 2x+2y as 2y+2x what operation will undo that +2x ?

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anonymous
  • anonymous
subtract 2 from both sides?
jim_thompson5910
  • jim_thompson5910
2x actually
jim_thompson5910
  • jim_thompson5910
so we will have 2y = 8 - 2x which is the same as 2y = -2x + 8
jim_thompson5910
  • 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
  • jim_thompson5910
hint: 2y means "2 times y"
anonymous
  • anonymous
divide 2 from both sides?
jim_thompson5910
  • jim_thompson5910
divide both sides by 2, yes
jim_thompson5910
  • jim_thompson5910
what do you get when you do this?
anonymous
  • anonymous
y = -2x +4?
jim_thompson5910
  • jim_thompson5910
you have to divide EVERY term by 2, not just the 8
anonymous
  • anonymous
y=x+4?
jim_thompson5910
  • 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
  • jim_thompson5910
x+4 is close, but no
anonymous
  • anonymous
x+3?
jim_thompson5910
  • jim_thompson5910
you had the +4 part correct
jim_thompson5910
  • jim_thompson5910
the "x" part was incorrect
anonymous
  • anonymous
why is x incorect?
jim_thompson5910
  • jim_thompson5910
you should divide -2x by 2 to get ????
anonymous
  • anonymous
x?
jim_thompson5910
  • jim_thompson5910
nope not x, you are thinking of 2x divided by 2
anonymous
  • anonymous
isnt that the same thing??
anonymous
  • anonymous
-x?
jim_thompson5910
  • jim_thompson5910
yes -x
jim_thompson5910
  • jim_thompson5910
so we will have y = -x + 4
jim_thompson5910
  • jim_thompson5910
2x + 2y = 8 turns into y = -x + 4 when you solve for y
jim_thompson5910
  • jim_thompson5910
so y = -x + 4 and 2x + 2y = 8 are equivalent (ie the same exact equations)
anonymous
  • anonymous
thank you for your help
jim_thompson5910
  • jim_thompson5910
another term for this is "dependent"
jim_thompson5910
  • jim_thompson5910
yw

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