Question

Solve the system of equation by Gauss –Jacobi me

thod.

27x + 6y – z = 85

6x + 15y + 2z = 72

x + y = 54z = 110​

Answer 1

Answer:

answer

Step-by-step explanation:

mark me brillent

Answer 2

Answer:  $x=\frac{85}{27}$,  $y=\frac{24}{5}$ and  $z=\frac{55}{27}$.

Step-by-step explanation:

• Given:

                   $27x + 6y-z = 85\\6x + 15y + 2z = 72\\x + y + 54z = 110$

• To find: Value of x, y and z by Gauss-Jacobi method.
• Solution:

         $27x + 6y-z=85$

     ⇒ $27x=85-6y+z$

     ⇒ $x=\frac{1}{27}[85-6y+z]$

     Putting y=0 and z=0.

     ⇒ $x=\frac{85}{27}$

again,

         $6x+15y+2z=72$

     ⇒ $15y=72-6x-2z$

     ⇒ $y=\frac{1}{15}[72-6x-2z]$

Putting x=0 and z=0.

     ⇒ $y=\frac{72}{15}=\frac{24}{5}$

again,

         $x+y+54z=110$

     ⇒ $54z=110-x-y$

     ⇒ $z=\frac{1}{54}[110-x-y]$

Putting x=0 and y=0.

     ⇒ $z=\frac{110}{54}=\frac{55}{27}$

So, the value of  $x=\frac{85}{27}$,  $y=\frac{24}{5}$ and  $z=\frac{55}{27}$.

• Hence, the values are as above.

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