anonymous
  • anonymous
7x-y-5z=5 6x+y-z=7 3x+y-7x=7 need help solving, please explain steps
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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KingGeorge
  • KingGeorge
In the last equation, is that \(3x+y-7z=7\)?
anonymous
  • anonymous
yes
KingGeorge
  • KingGeorge
First, in the process of solving it, notice that equation 1 has a \(-y\) term, while equation 2 has \(+y\) term. Thus, if you add the equations together you get a \(0y =0\) term where the \(y\) used to be.

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KingGeorge
  • KingGeorge
\[\begin{matrix}7x-y-5z=5\\6x+y-z=7\\ \text{______________}\\13x-6z=12\end{matrix}\]
KingGeorge
  • KingGeorge
Let's call this equation 4.
KingGeorge
  • KingGeorge
My apologies. We don't want to get rid of x, we want to get rid of y here. Fortunately, both equation 2 and 3 have a \(+y\) term so we just subtract the two equations.\[\begin{matrix}6x+y-z=7\\ - \quad 3x+y-7z=-7\\ \text{______________________}\\3x+6z=14\end{matrix}\]
KingGeorge
  • KingGeorge
Let's call this equation 5.
KingGeorge
  • KingGeorge
Now we see that equation 4 has a \(-6z\) term, and equation 5 has a \(+6z\) term. Thus we can add them again.\[\begin{matrix}\:\:\quad13x-6z=12\\ - \quad 3x+6z=14\\ \text{______________________}\\16x=26\end{matrix}\]From here we can easily solve for \(x=26/16=13/8\)
KingGeorge
  • KingGeorge
Plug this value for x back into equation 5. \[3(13/8)+6z=14\]So we can find that \(z=73/48\)
KingGeorge
  • KingGeorge
If we plug both of these values into equation 2 (any of the first 3 should work) we get \[6(13/8) +y -(73/48)=7\]We finally get that \(y=175/48\)
anonymous
  • anonymous
I can solve for the x term is 3/4, but I don't seem to be getting the other variables correct okay, thanks
KingGeorge
  • KingGeorge
I think I made some error, so you may be correct. Let me recheck my work.
KingGeorge
  • KingGeorge
You are correct. \(x=3/4\)
KingGeorge
  • KingGeorge
Equation 5 should rather be\[3x+6z=0\]
KingGeorge
  • KingGeorge
Then, \[\begin{matrix}\quad \:\:13x-6z=12\\ \quad 3x+6z=0\\ \text{___________________}\\16x=12\end{matrix}\]So \(x=3/4\)
KingGeorge
  • KingGeorge
Then substituting into equation 5, \[3(3/4) +6z=0\]Means that \(z=-3/8\)
KingGeorge
  • KingGeorge
Substituting both of these into equation 2, we finally get that \[6(3/4)+y-(-3/8)=7\]Which means that \(y=17/8\).
KingGeorge
  • KingGeorge
Sorry about the confusion :( I wrote down the wrong equations on my end.

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