Question

Solve 5x-y-2z = 142,x-3y-z = -30,2x-y-3z = 5 by Gauss

elimination method.​

Answer 1

The required values of x, y, and z are :

x =  48.8276

y = 11.1034

z =  45.5172

Given that;

5x-y-2z = 142

x-3y-z = -30

2x-y-3z = 5

To find;

The solution of the given equations by the Gauss elimination method.​

Solution;

We have,

5x-y-2z = 142...(1)

x-3y-z = -30...(2)

2x-y-3z = 5...(3)

Eliminating x from (2) and (3) using equation (1) we get,

x - $\frac{1}{5}$y - $\frac{2}{5}$z  = $\frac{142}{5}$...(4)

- $\frac{14}{5} y$ - $\frac{3}{5} z$ = - $\frac{292}{5}$...(5)

- $\frac{3}{5}y$ - $\frac{11}{5} z$ = $\frac{- 534}{5}$...(6)

Eliminating y from equation (6) we get,

$\frac{145}{5}z$ = $\frac{6600}{5}$

z = $\frac{6600}{145}$ = 45.5172

Thus, from equation (5) we get,

- $\frac{14}{5} y$ - $\frac{3}{5}$ x  $\frac{6600}{145}$ = - $\frac{292}{5}$

y = $\frac{-5}{14}$( $\frac{19800}{725}$ - $\frac{292}{5}$) = 11.1034

From equation (4) we get,

x - $\frac{1}{5}$( 11.1034 - $\frac{2}{5}$(  45.5172) = 48.8276

Hence the solution is :

x =  48.8276

y = 11.1034

z =  45.5172

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