Question

the values of x,y,z in the following system of equations by gauss elimination method 2x+y-3z=-10,-2y+z=-2,z=6​

Answer 1

Answer:

z=6

y=4

x=2

please do check

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Answer 2

Answer:

The values are x = 2, y = 4 and z = 6.

Step-by-step explanation:

The given equations are

2x+y-3z = -10

-2y+z = -2

z = 6

The given equations in the matrix form are given, by

$A=\left[\begin{array}{4444}2&1&-3&-10\\0&-2&1&-2\\0&0&1&6\end{array}\right]$  $R_{1}/2$ → $R_{1}$  

   $=\left[\begin{array}{4444}1&0.5&-0.5&-5\\0&-2&1&-2\\0&0&1&6\end{array}\right]$  $R_{2} /(-2)$ → $R_{2}$

   $=\left[\begin{array}{4444}1&0.5&-0.5&-5\\0&1&-0.5&1\\0&0&1&6\end{array}\right]$  $R_{1}- 0.5R_{2}$ → $R_{1}$

   $=\left[\begin{array}{4444}1&0&-1.25&-5.5\\0&1&-0.5&1\\0&0&1&6\end{array}\right]$

      $R_{1}+1.25R_{3}$ → $R_{1}$

      $R_{2} + 0.5R_{3}$ → $R_{2}$

  $=\left[\begin{array}{4444}1&0&1&2\\0&1&0&4\\0&0&1&6\end{array}\right]$      

Therefore the values are x = 2, y = 4, z = 6.