CderaAlien
  • CderaAlien
I don't understand... So, I had the equations: −3x − 2y = 4 −x + y = 3 and it wanted me to show what point represented the system solution shown. Since there wasn't any opposite coefficients within the equations, I had to multiply because none of the coefficients were opposites. So, the next step was to multiply the entire second equation by positive 2. Why did chose the second equation, and multiply it by 2? I don't understand.
Mathematics
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SOLVED
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katieb
  • katieb
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CderaAlien
  • CderaAlien
Does anybody honestly know? lol
CderaAlien
  • CderaAlien
@AlexandervonHumboldt2
jim_thompson5910
  • jim_thompson5910
notice in the first equation you have `-2y` in the second equation, you have `y` which is really the same as `1y`

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jim_thompson5910
  • jim_thompson5910
adding the equations gives -2y+1y = 1y we want to add the equations so that the y terms cancel out we can do this by multiplying everything in equation 2 by 2
jim_thompson5910
  • jim_thompson5910
`−x + y = 3` will turn into `-2x+2y = 6` after you multiply both sides by 2
jim_thompson5910
  • jim_thompson5910
so we have this system now -3x-2y = 4 -2x+2y = 6 adding up the equations gives -5x+0y = 10 which is the same as -5x = 10 The y terms are completely gone and you can solve for x to get x = ???
jim_thompson5910
  • jim_thompson5910
hopefully that makes sense @CderaAlien ?
CderaAlien
  • CderaAlien
@jim_thompson5910 reading now, if you don't min after I read this could you explain something else to me? I would kindly appreciate it!
CderaAlien
  • CderaAlien
*mind
jim_thompson5910
  • jim_thompson5910
sure, what other question did you have?
CderaAlien
  • CderaAlien
In the question: In the following system, what number should the first equation be multiplied by to begin solving using elimination? x + 3y = 12 −5x + 6y = 4 Does the same thing you just explained with the above problem apply to this problem?
jim_thompson5910
  • jim_thompson5910
first ask yourself: which variable do I want to eliminate? x? or y?
CderaAlien
  • CderaAlien
I believe the x variable
jim_thompson5910
  • jim_thompson5910
ok so adding the x terms we see x plus -5x = 1x plus -5x = -4x we want the sum of the x terms to be 0x, so the x terms go away
CderaAlien
  • CderaAlien
Here is the answer to the question: Multiply the first equation by 5. 5(x) + 5(3y) = 5(12) 5x + 15y = 60 The x terms become opposites and cancel with addition. 5x + 15y = 60 −5x + 6y = 4
jim_thompson5910
  • jim_thompson5910
so multiply everything in equation 1 by 5 that will turn `x+3y = 12` into `5x + 15y = 60` giving you this new system 5x + 15y = 60 -5x+6y = 4
jim_thompson5910
  • jim_thompson5910
that is correct
CderaAlien
  • CderaAlien
I just don't understand why they multiplied by 5....so confused.
jim_thompson5910
  • jim_thompson5910
because that turned the `x` into `5x` now we can say 5x + (-5x) = 0x
jim_thompson5910
  • jim_thompson5910
in the x term in the first equation, we have x or 1x the coefficient is 1 now we ask ourselves: what goes in the blank? 1 times _______ = 5 the answer to that question is: 5 so we have 1*5 = 5 and we do this to every term in the first equation
CderaAlien
  • CderaAlien
Oh, so basically they chose, because 5 would eliminate the opposite coefficients?
jim_thompson5910
  • jim_thompson5910
that is correct
CderaAlien
  • CderaAlien
as in turn x + 3y = 12 into 5x + 15y = 60 to eliminate the 5x and -5x @jim_thompson5910
CderaAlien
  • CderaAlien
ahh, I see. Thank you!!!
jim_thompson5910
  • jim_thompson5910
I'm glad it makes sense now. You're welcome

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