Answers

2014-03-26T15:48:40+01:00
2x+y-3z=5    EQ 1
3x-2y-2z=5    EQ2
5x-3y-z=16    EQ3
from  eq 1
2x+y-3z=5
y=5+3z-2x eq4
subst. y=5+3z-2x for y in eq 2
3x-2(5+3z-2x)-2z=5
3x-10-6z+4x-2z=5
7x-8z-10=5
7x-8z=15  eq 5

also subst. y=5+3z-2x for y in eq 3
5x-3(5+3z-2x)-z=16
5x-15-9z+6x-z=16
11x-10z=31  eq6

from eq 5 and 6
7x-8z=15
11x-10z=31
frm eq 5
7x=15+8z
x=15+8z/7
subst. x=15+8z/7 for x in eq 6
11(15+8z/7)-10z=31
165+88z/7-10z=31
165+88z-70z=31x7
165+18z=217
18z=217-165
x=52/18
x=26/9
subst. 26/9 for x in eq6
11(26/9)-10z=31
286/9-10z=31
286-90z=279
-9z=279-286
z= -7/-9
z= 7/9

subst. x=26/9  and z=7/9 in eq. 4
y=5+3z-2x
y=5+3(7/9)-2(26/9)
y= 5+21/9-52/9
9y=45+21-52
9y=14
y=14/9

so therefore: x=26/9, y=14/9, z=7/9






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