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# system problem

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Find the ordered triplet (x,y,z) for the following system of equations:

x + 3y + 2z = 1

-3x + y + 5z = 10

-2x + 3y + z = 7

May 18, 2021

#1
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well, I came back again to this site.

you see the first and the last equation?

Subtract them such that the 3y is canceled out.

\$x+3y+2z-(-2x+3y+z)=1-7\$
\$3x+z = -6\$

Neext, multiply the middle equation by \$3\$ to make \$-9x+3y+15z=30\$.

then, subtract the last equation from it to get:
\$-2x+3y+z-(-9x+3y+15z) = 7-30\$
which is equal to \$7x-14z=-23\$

So here are the two equations we have:

\$3x+z = -6\$

\$7x-14z=-23\$

Take the first equation and find z, which is \$z=-6-3x\$. Put the Z inside the second equation, \$7x-14(-6-3x) = -23\$, which is \$7x+84+42x = -23\$, or simply \$49x=-107\$

So, \$x\$ is equal to \$-107/49\$

Now, find z. Insert x into the equation, and get that \$3(-107/49) + z = -6\$, which means that \$z=27/49\$.

Insert those two into the second ever equation to find y:
\$6 and 27/49 + y + 2 and 37/49= 10\$, which in the end is equal to \$y=9 and 15/49\$

so the answer you seek is \$(-107/49,27/49, 456/49)\$

May 18, 2021
#2
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thanks for the clear, detailed explanation

word counter

pipahaha  May 18, 2021
#3
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Your welcome! Have a nice night or day or afternoon!

OofPirate  May 18, 2021
#4
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I get the following: May 18, 2021