Q. 45 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The system is inconsistent

Step 1: Given information

We are given a system of equation as

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

Step 2: Add equation 1 and 2

We get,

$x-y-z=1+2z+3y+z=23x+2y=3$

But from equation 3 we have $3x+2y=0$

As same equation cannot have different values

Hence the system is inconsisitent

Step 3: Conclusion

The given system of equation is inconsistant