Question

Equation x+y+z=6 , x-y+z=2 , 2x+y-z=1 have solution :
a) x=1 ,y=1, z=1
b) x=1 ,y=3 ,z=2
c) x=2, y=1 ,z=3
d) x=1, y=2 ,z=3​

Answer 1

Step-by-step explanation:

have,

x+y+z=6,x−y+z=2,2x+y−z=1

Thus A=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

2

1

−1

1

1

1

−1

∣

∣

∣

∣

∣

∣

∣

∣

X=

∣

∣

∣

∣

∣

∣

∣

∣

x

y

z

∣

∣

∣

∣

∣

∣

∣

∣

,B=

∣

∣

∣

∣

∣

∣

∣

∣

6

2

1

∣

∣

∣

∣

∣

∣

∣

∣

Now Solve A to get A=6

Now x=

A

A

x

=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

2

1

−1

1

1

1

−1

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

6

2

1

1

−1

1

1

1

−1

∣

∣

∣

∣

∣

∣

∣

∣

=

6

6

=1

y=

A

A

y

=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

2

1

−1

1

1

1

−1

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

1

1

2

6

2

1

1

1

−1

∣

∣

∣

∣

∣

∣

∣

∣

=

6

12

=2

z=

A

A

z

=

∣

∣

∣

∣

∣

∣

∣

∣

1

1

2

1

−1

1

1

1

−1

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

1

1

2

1

−1

1

6

2

1

∣

∣

∣

∣

∣

∣

∣

∣

=

6

18

=3

Thus x=1,y=2,z=3

Answer 2

Answer:

d is the right answer.....