Chapter 1, Problem 17CR

To determine

To calculate : The given system of equations for $x,y,z$ is to be calculated

Answer to Problem 17CR

  $x=-16$

  $y=12$

  $z=10$

Explanation of Solution

Given information : The given system of equations is:

  $x+2z=4$

  $x+y+z=6$

  $3x+3y+4z=28$

Formula used : Elimination method

In which we add or subtract the two equations together in the system to eliminate one of the variable.

Calculation : Considering first two equations:

  $x+2z=4$

  $x+y+z=6$

Subtract above two equations, we get

  $y-z=2$

Considering second and third equation:

  $x+y+z=6$

  $3x+3y+4z=28$

Multiply equation $x+y+z=6$ by 3 then subtract it from equation $3x+3y+4z=28$ , we get

  $z=10$

Putting the value of $z=10$ in equation $y-z=2$ , we get

  $y=12$

Now, finally put $y=12$ and $z=10$ in equation $x+y+z=6$ , we get

  $x=-16$

Check:

Put the value of $x=-16$ , $y=12$ and $z=10$ in all the above given equations we get the three true statements:

  $\begin{array}{l}4=4\\ 6=6\\ 28=28\end{array}$