Q. 47 - Precalculus Enhanced with Graphing Utilities

Question

Solve each system of equations. If the system has no solution, say that it is inconsistent. 

$$\begin{gathered} x-y-z=1 \\ -x+2y-3z=-4 \\ 3x-2y-7z=0 \end{gathered}$$

Step-by-Step Solution

Answer

The solution of the given system of equation is 

$(x,y,z)=\left\{\right(5z-2,4z-3,z)/z\in R\}$

Step 1: Given information

We are given a system of equation

$$\begin{gathered} x-y-z=1 \left(1\right) \\ -x+2y-3z=-4 \left(2\right) \\ 3x-2y-7z=0 \left(3\right) \end{gathered}$$

Step 2: Add equation 1 and 2

We get,

$x-y-z=1-x+2y-3z=-4y-4z=-3$

We get, $y-4z=-3$

Hence $y=4z-3$

Step 3: add equation 2 and 3

We get,

$-x+2y-3z=-4+3x-2y-7z=02x-10z=-4$

Hence $$\begin{gathered} 2x-10z=-4 \\ and x=5z-2 \end{gathered}$$

Step 4: Conclusion

The solution set of the given system of equation is

$(x,y,z)=\left\{\right(5z-2,4z-3,z)/z\in R\}$