Chapter 1, Problem 12CR

To determine

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

Answer to Problem 12CR

  $x=4,y=-2,z=1$

Explanation of Solution

Given information :

Given system equations are:

  $x+y+z=3$

  $-x+3y+2z=-8$

  $x=4z$

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

  $x+y+z=3$

  $-x+3y+2z=-8$

Add both the above equations, we get

  $4y+3z=-5$

Considering second and third equation

  $-x+3y+2z=-8$

  $x=4z$

By putting, $x=4z$ in equation $-x+3y+2z=-8$ we get,

  $y+5z=3$

Now taking the two equations as written below:

  $4y+3z=-5$

  $y+5z=3$

On solving above two equations we get,

  $z=1$

Then we put $z=1$ in equation $x=4z$ we get

  $x=4$

By putting, $x=4$

  $z=1$ in equation $x+y+z=3$ , we get

  $y=-2$

Check:

By putting, $x=4$

  $y=-2$ and $z=1$ in all the given system of equations, we get the three true statements: $3=3,-8=-8and4=4$