1. Solve Equations 2x+5y=21,x+2y=8 using Gauss Jacobi method

Solution:
Total Equations are `2`

`2x+5y=21`

`x+2y=8`


From the above equations
`x_(k+1)=1/2(21-5y_(k))`

`y_(k+1)=1/2(8-x_(k))`

Initial gauss `(x,y) = (0,0)`

Solution steps are
`1^(st)` Approximation

`x_1=1/2[21-5(0)]=1/2[21]=10.5`

`y_1=1/2[8-(0)]=1/2[8]=4`

`2^(nd)` Approximation

`x_2=1/2[21-5(4)]=1/2[1]=0.5`

`y_2=1/2[8-(10.5)]=1/2[-2.5]=-1.25`

`3^(rd)` Approximation

`x_3=1/2[21-5(-1.25)]=1/2[27.25]=13.625`

`y_3=1/2[8-(0.5)]=1/2[7.5]=3.75`

`4^(th)` Approximation

`x_4=1/2[21-5(3.75)]=1/2[2.25]=1.125`

`y_4=1/2[8-(13.625)]=1/2[-5.625]=-2.8125`

`5^(th)` Approximation

`x_5=1/2[21-5(-2.8125)]=1/2[35.0625]=17.5312`

`y_5=1/2[8-(1.125)]=1/2[6.875]=3.4375`

`6^(th)` Approximation

`x_6=1/2[21-5(3.4375)]=1/2[3.8125]=1.9062`

`y_6=1/2[8-(17.5312)]=1/2[-9.5312]=-4.7656`

`7^(th)` Approximation

`x_7=1/2[21-5(-4.7656)]=1/2[44.8281]=22.4141`

`y_7=1/2[8-(1.9062)]=1/2[6.0938]=3.0469`


Equations are Divergent...
Intertions are tabulated as below

Iteration	x	y
1	10.5	4
2	0.5	-1.25
3	13.625	3.75
4	1.125	-2.8125
5	17.5312	3.4375
6	1.9062	-4.7656
7	22.4141	3.0469

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