Chapter 1, Problem 15CR

To determine

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

Answer to Problem 15CR

The given system of equations has no solution.

Explanation of Solution

Given information: The given system of equation is:

  $x+4y-2z=3$

  $x+3y+7z=1$

  $2x+9y-13z=2$

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:

  $x+4y-2z=3$

  $x+3y+7z=1$

Subtract the above two equations, we get

  $y-9z=2$

Considering second and third equations:

  $x+3y+7z=1$

  $2x+9y-13z=2$

Multiply the equation $x+3y+7z=1$ by 2 then subtract it from the equation $2x+9y-13z=2$ we get,

  $y=9z$

Now, put the equation $y=9z$ in the equation $y-9z=2$ , we get

  $0=2$ , which is a false statement.

So, the system has no solution.