5x-y+4z=14
-5x-y-2z=-10
-5x+3y-6z=-18
Solving this by linear combination?
5x-y+4z=14
-5x-y-2z=-10
-5x+3y-6z=-18
Solving this by linear combination?
(1):5x−y+4z=14(2):−5x−y−2z=−10(3):−5x+3y−6z=−18(1)+(2):5x−y+4z−5x−y−2z=14−10−2y+2z=4|:2−y+z=2(I):z=2+y(1)+(3):5x−y+4z−5x+3y−6z=14−182y−2z=−4|:(−2)−y+z=2(II):z=2+y|(II)=(I) !!!(1):5x−y+4z=14|z=2+y5x−y+4⋅(2+y)=14(III):5x+3y=6(2):−5x−y−2z=−10|z=2+y−5x−y−2⋅(2+y)=−10−5x−3y=−6|⋅(−1)(IV):5x+3y=6|(IV)=(III) !!!
Solution:
Let t∈R and we set z=t
(I):z=2+y|z=tt=2+yy=t−2(III):5x+3y=6|y=t−25x+3⋅(t−2)=65x+3t−6=65x+3t=125x=12−3t5x=12−3t|:5x=125−35t
summary:
t∈Rx=125−35ty=t−2z=t
5x-y+4z=14
-5x-y-2z=-10
-5x+3y-6z=-18
Solving this by linear combination?
(1):5x−y+4z=14(2):−5x−y−2z=−10(3):−5x+3y−6z=−18(1)+(2):5x−y+4z−5x−y−2z=14−10−2y+2z=4|:2−y+z=2(I):z=2+y(1)+(3):5x−y+4z−5x+3y−6z=14−182y−2z=−4|:(−2)−y+z=2(II):z=2+y|(II)=(I) !!!(1):5x−y+4z=14|z=2+y5x−y+4⋅(2+y)=14(III):5x+3y=6(2):−5x−y−2z=−10|z=2+y−5x−y−2⋅(2+y)=−10−5x−3y=−6|⋅(−1)(IV):5x+3y=6|(IV)=(III) !!!
Solution:
Let t∈R and we set z=t
(I):z=2+y|z=tt=2+yy=t−2(III):5x+3y=6|y=t−25x+3⋅(t−2)=65x+3t−6=65x+3t=125x=12−3t5x=12−3t|:5x=125−35t
summary:
t∈Rx=125−35ty=t−2z=t