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# System

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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

Aug 17, 2021

#1
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The solution is (x,y,z) = (2,3,-2).

Aug 17, 2021
#2
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Find the ordered triplet (x,y,z) for the system of equations.

Hello Guest!

$$x + 3y + 2z = 1\ |\ \times 2$$

-3x + y + 5z = 10

-2x + 3y + z = 7

$$2x+6y+4z=2$$

$$\underline{-2x + 3y + z = 7}$$

$$9y+5z=9\ |\ \times 10$$

$$x + 3y + 2z = 1\ |\ \times 3\\ \ \\ 3x+9y+6z=3$$

$$\underline{ -3x + y + 5z = 10}$$

$$10y+11z=13\ |\ \times 9$$

$$90y+50z=90$$

$$\underline{90y+99z=117}$$

$$49z=27$$

$$z=\dfrac{27}{49}$$

$$10y+11z=13\ |\ insert\ z$$

$$10y+\dfrac{11\cdot 27}{49}=13\\ 490y=13\cdot49-11\cdot 27=340$$

$$y=\dfrac{34}{49}$$

$$x + 3y + 2z = 1\\ x=1-3y-2z\ |\ insert\ y\ and\ z\\ x=1-\frac{3\cdot 34}{49}-\frac{2\cdot 27}{49}\\ 49x=49-3\cdot 34-2\cdot27\\ 49x=-107$$

$$x=-\dfrac{107}{49}$$

$$(x,y,z)=(-\dfrac{107}{49},\dfrac{34}{49},\dfrac{27}{49})$$

!

Aug 17, 2021
edited by asinus  Aug 17, 2021