Question

Find the solution to the system of equations? 4x-3y-z=3 , -3x+5y+z=9, x+2z=6

Answer 1

Answer:

is this the one?

Step-by-step exExplanation:

Adding third equation to first one,

7

x

+

5

y

+

z

+

x

−

6

y

−

z

=

0

−

18

or  

8

x

−

y

=

−

18

.  

(

1

)

Adding 2 times of third one to second one,

−

x

+

3

y

+

2

z

+

2

⋅

(

x

−

6

y

−

z

)

=

16

−

2

⋅

18

or  

x

−

9

y

=

−

20

 

(

2

)

Substracting 8 times of  

(

2

)

from  

(

1

)

,

8

x

−

y

−

8

⋅

(

x

−

9

y

)

=

−

18

−

8

⋅

(

−

20

)

71

y

=

142

, so  

y

=

2

Hence,

x

−

9

⋅

2

=

−

20

or  

x

−

18

=

−

20

, so  

x

=

−

2

Thus,

7

⋅

(

−

2

)

+

5

⋅

2

+

z

=

0

or  

z

−

4

=

0

, so  

z

=

4Explanation:

Adding third equation to first one,

7

x

+

5

y

+

z

+

x

−

6

y

−

z

=

0

−

18

or  

8

x

−

y

=

−

18

.  

(

1

)

Adding 2 times of third one to second one,

−

x

+

3

y

+

2

z

+

2

⋅

(

x

−

6

y

−

z

)

=

16

−

2

⋅

18

or  

x

−

9

y

=

−

20

 

(

2

)

Substracting 8 times of  

(

2

)

from  

(

1

)

,

8

x

−

y

−

8

⋅

(

x

−

9

y

)

=

−

18

−

8

⋅

(

−

20

)

71

y

=

142

, so  

y

=

2

Hence,

x

−

9

⋅

2

=

−

20

or  

x

−

18

=

−

20

, so  

x

=

−

2

Thus,

7

⋅

(

−

2

)

+

5

⋅

2

+

z

=

0

or  

z

−

4

=

0

, so  

z

=

4planation: