anonymous
  • anonymous
can someone show me step by step how to do this? If you were to use the elimination method to solve the following system, choose the new system of equations that would result after the variable z is eliminated in the first and second equations, then the second and third equations. x + y – 3z = –8 2x + 2y + z = 12 3x + y – z = –2
Mathematics
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jamiebookeater
  • jamiebookeater
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jdoe0001
  • jdoe0001
ok, well you have x + y – 3z = –8 2x + 2y + z = 12 3x + y – z = –2 so, the idea is that you will pick a "pair" of equations firstly from there eliminate ONE variable, say "z" and you'd get a 1ST NEWLY FORMED EQUATION with only "x" and "y" so, you go back to the 3 equations and pick "another pair", and eliminate "z" again and you'd get a 2ND NEWLY FORMED EQUATION with only "x" and "y" so, now you'd end up with 2 NEW EQUATIONS with only "x" and "y" and you work those like any 2x2 system of equations :)
jdoe0001
  • jdoe0001
gsheila27 confused?
anonymous
  • anonymous
kind of. if u were to do it step by step i would understand it better @jdoe0001

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jdoe0001
  • jdoe0001
ok
jdoe0001
  • jdoe0001
$$ \begin{matrix} x &+ y &– 3z &= –8\\ 2x &+ 2y &+ z &= 12\\ 3x &+ y &– z &= –2 \\ \end{matrix}\\ \color{blue}{\text{so, let's take the 1st and 2nd}}\\ ---------------------\\ \begin{matrix} x &+ y &– 3z &= –8 \\ 2x &+ 2y &+ z &= 12& \times 3\\ \end{matrix}\\ ----------------------\\ \begin{matrix} x &+ y &– 3z &= –8\\ 6x &+ 6y &+ 3z &= 36 & \times 3\\ \hline \\ 7x& +7y & +0 &= 28 \end{matrix} $$
jdoe0001
  • jdoe0001
so you end up with 1st NEW EQUATION
anonymous
  • anonymous
ohk :) @jdoe0001
jdoe0001
  • jdoe0001
$$ \begin{matrix} x &+ y &– 3z &= –8\\ 2x &+ 2y &+ z &= 12\\ 3x &+ y &– z &= –2 \\ \end{matrix}\\ \color{blue}{\text{so, let's take the 1st and 3rd}}\\ ---------------------\\ \begin{matrix} x &+ y &– 3z &= –8\\ 3x &+ y &– z &= –2 & \times -3\\ \end{matrix}\\ ----------------------\\ \begin{matrix} 2x &+ y &– 3z &= –8\\ -9x &-3y &+3z &= 6 & \times -3\\ \hline \\ -7x& -2y & +0 & = -2 \end{matrix} $$
jdoe0001
  • jdoe0001
so , now you have the 2nd NEW EQUATION
jdoe0001
  • jdoe0001
now you just use the NEW EQUATIONS with only "x" and "y" solve by elimination for either :) so, you'll get one and the other grab both and plug them on any of the 3 equations, and solve for "z"
anonymous
  • anonymous
so i would use the -7x -2y etc..... with the last equation ? @jdoe0001
jdoe0001
  • jdoe0001
you'd use the 2 NEW EQUATIONS, which do not contain "z" just "x" and "y" so they're just a system of 2 variables
jdoe0001
  • jdoe0001
so you'd solve say 7x +7y = 28 -7x -26 =-2
jdoe0001
  • jdoe0001
if you add them up, right off, "x" drops off, so, that came up quite simple
anonymous
  • anonymous
ty so much
jdoe0001
  • jdoe0001
yw

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