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5x-y+4z=14

-5x-y-2z=-10

-5x+3y-6z=-18

Solving this by linear combination?

 Nov 23, 2016

Best Answer 

 #1
avatar+26397 
+10

5x-y+4z=14

-5x-y-2z=-10

-5x+3y-6z=-18

Solving this by linear combination?

 

(1):5xy+4z=14(2):5xy2z=10(3):5x+3y6z=18(1)+(2):5xy+4z5xy2z=14102y+2z=4|:2y+z=2(I):z=2+y(1)+(3):5xy+4z5x+3y6z=14182y2z=4|:(2)y+z=2(II):z=2+y|(II)=(I) !!!(1):5xy+4z=14|z=2+y5xy+4(2+y)=14(III):5x+3y=6(2):5xy2z=10|z=2+y5xy2(2+y)=105x3y=6|(1)(IV):5x+3y=6|(IV)=(III) !!!

 

Solution:

Let tR and we set z=t

 

(I):z=2+y|z=tt=2+yy=t2(III):5x+3y=6|y=t25x+3(t2)=65x+3t6=65x+3t=125x=123t5x=123t|:5x=12535t

 

summary:
tRx=12535ty=t2z=t

 

laugh

 Nov 23, 2016
 #1
avatar+26397 
+10
Best Answer

5x-y+4z=14

-5x-y-2z=-10

-5x+3y-6z=-18

Solving this by linear combination?

 

(1):5xy+4z=14(2):5xy2z=10(3):5x+3y6z=18(1)+(2):5xy+4z5xy2z=14102y+2z=4|:2y+z=2(I):z=2+y(1)+(3):5xy+4z5x+3y6z=14182y2z=4|:(2)y+z=2(II):z=2+y|(II)=(I) !!!(1):5xy+4z=14|z=2+y5xy+4(2+y)=14(III):5x+3y=6(2):5xy2z=10|z=2+y5xy2(2+y)=105x3y=6|(1)(IV):5x+3y=6|(IV)=(III) !!!

 

Solution:

Let tR and we set z=t

 

(I):z=2+y|z=tt=2+yy=t2(III):5x+3y=6|y=t25x+3(t2)=65x+3t6=65x+3t=125x=123t5x=123t|:5x=12535t

 

summary:
tRx=12535ty=t2z=t

 

laugh

heureka Nov 23, 2016
 #2
avatar
0

are you sure thats right

 Nov 27, 2016

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