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## Answers

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