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Click here to Find the value of h,k for which the system of equations has a Unique or Infinite or no solution calculator
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Solution
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Solution provided by AtoZmath.com
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Solving systems of linear equations using Gauss Seidel method calculator
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 1. `2x+y+z=5,3x+5y+2z=15,2x+y+4z=8`
2. `2x+5y=16,3x+y=11`
3. `2x+5y=21,x+2y=8`
4. `2x+y=8,x+2y=1`
5. `2x+3y-z=5,3x+2y+z=10,x-5y+3z=0`
6. `x+y+z=3,2x-y-z=3,x-y+z=9`
7. `x+y+z=7,x+2y+2z=13,x+3y+z=13`
8. `2x-y+3z=1,-3x+4y-5z=0,x+3y-6z=0`
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Example1. Solve Equations 2x+y=8,x+2y=1 using Gauss Seidel methodSolution: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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