Chapter 1, Problem 13CR

To determine

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

Answer to Problem 13CR

  $x=-\frac{4}{3},y=-\frac{17}{3},z=\frac{26}{3}$

Explanation of Solution

Given information : The given system of equation is:

  $2x-5y-z=17$

  $x+y+z=19$

  $-4x+6y+z=-20$

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

  $2x-5y-z=17$

  $x+y+z=19$

Multiply second equation by 2 and subtract it from first equation, we get

  $y+z=3$

Now, considering second and third equation

  $x+y+z=19$

  $-4x+6y+z=-20$

Multiply the equation $x+y+z=19$ by 4 and add it into equation $-4x+6y+z=-20$ , we get

  $10y+13z=56$

Now, multiply the equation $y+z=3$ by 10 and subtract it from $10y+13z=56$ , we get

  $z=\frac{26}{3}$

Put the value $z=\frac{26}{3}$ in equation $y+z=3$ , we get

  $y=-\frac{17}{3}$

Now, put $y=-\frac{17}{3}$ and $z=\frac{26}{3}$ in equation $x+y+z=19$ , we get

  $x=-\frac{4}{3}$

Check: By putting, $x=-\frac{4}{3}$ , $y=-\frac{17}{3}$ and $z=\frac{26}{3}$ in all the given system of equations, we get the three true statements: $17=17$ , $19=19$ and $-20=-20$