Chapter 1, Problem 16CR

To determine

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

Answer to Problem 16CR

  $x=-11$

  $y=-8$

  $z=3$

Explanation of Solution

Given information: The given system of equation is:

  $x-y+3z=6$

  $x-2y=5$

  $2x-2y+5z=9$

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:

  $x-y+3z=6$

  $x-2y=5$

Subtract the above two equations, we get

  $y+3z=1$

Considering the second and third equation

  $x-2y=5$

  $2x-2y+5z=9$

Multiply the equation $x-2y=5$ by 2 subtract it from the equation $2x-2y+5z=9$ , we get

  $2y+5z=-1$

Multiply the equation $y+3z=1$ by 2 then subtract it from the equation $2y+5z=-1$ , we get

  $z=3$

Put the value $z=3$ in equation $y+3z=1$ , we get

  $y=-8$

Finally, put $y=-8$ and $z=3$ in equation $x-y+3z=6$ , we get

  $x=-11$

Check:

Put the value $x=-11$ , $y=-8$ and $z=3$ in all the above given system of equations we get the three true statements:

  $6=6$

  $5=5$

  $9=9$