Chapter 1, Problem 14CR

To determine

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

Answer to Problem 14CR

  $$ The given system of equation has infinitely many solutions.

Explanation of Solution

Given information : The given system of equation is:

  $x+y+z=2$

  $2x-3y+z=11$

  $-3x+2y-2z=-13$

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

  $x+y+z=2$

  $2x-3y+z=11$

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

  $5y+z=-7$

Now, taking second and third equation

  $2x-3y+z=11$

  $-3x+2y-2z=-13$

Multiply the equation $2x-3y+z=11$ by 3 and the equation $-3x+2y-2z=-13$ by 2, then add both the equations, we get

  $5y+z=-7$

Considering equations

  $5y+z=-7$

  $5y+z=-7$

We get, $0=0$ which is a true statement.

So, the system has infinitely many solutions.