1. Solve Equations 2x+y=8,x+2y=1 using Gauss Seidel method

Solution:
Total Equations are `2`

`2x+y=8`

`x+2y=1`


From the above equations
`x_(k+1)=1/2(8-y_(k))`

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

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

Solution steps are
`1^(st)` Approximation

`x_1=1/2[8-(0)]=1/2[8]=4`

`y_1=1/2[1-(4)]=1/2[-3]=-1.5`

`2^(nd)` Approximation

`x_2=1/2[8-(-1.5)]=1/2[9.5]=4.75`

`y_2=1/2[1-(4.75)]=1/2[-3.75]=-1.875`

`3^(rd)` Approximation

`x_3=1/2[8-(-1.875)]=1/2[9.875]=4.9375`

`y_3=1/2[1-(4.9375)]=1/2[-3.9375]=-1.9688`

`4^(th)` Approximation

`x_4=1/2[8-(-1.9688)]=1/2[9.9688]=4.9844`

`y_4=1/2[1-(4.9844)]=1/2[-3.9844]=-1.9922`

`5^(th)` Approximation

`x_5=1/2[8-(-1.9922)]=1/2[9.9922]=4.9961`

`y_5=1/2[1-(4.9961)]=1/2[-3.9961]=-1.998`

`6^(th)` Approximation

`x_6=1/2[8-(-1.998)]=1/2[9.998]=4.999`

`y_6=1/2[1-(4.999)]=1/2[-3.999]=-1.9995`

`7^(th)` Approximation

`x_7=1/2[8-(-1.9995)]=1/2[9.9995]=4.9998`

`y_7=1/2[1-(4.9998)]=1/2[-3.9998]=-1.9999`


Solution By Gauss Seidel Method.
`x=4.9998~=5`

`y=-1.9999~=-2`

Iterations are tabulated as below

Iteration	x	y
1	4	-1.5
2	4.75	-1.875
3	4.9375	-1.9688
4	4.9844	-1.9922
5	4.9961	-1.998
6	4.999	-1.9995
7	4.9998	-1.9999

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