Question

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

$$\begin{gathered} 2x-2y+3z=6 \\ 4x-3y+2z=0 \\ -2x+3y-7z=1 \end{gathered}$$

Short answer

The system is inconcsistent

Step-by-step solution

Given information

We are given a system of equation

$$\begin{gathered} 2x-2y+3z=6\left(1\right) \\ 4x-3y+2z=0\left(2\right) \\ -2x+3y-7z=1\left(3\right) \end{gathered}$$

Add equation 2 and 3

We get,$4x-3y+2z=0-2x+3y-7z=12x-5z=1$

Hence$2x-5z=1$

Multiply equation 1 by 3 and equation 3 by 2The add both the equation

We get,

$$\begin{gathered} 3(2x-2y+3z=6) \\ 6x-6y+9z=18\left(4\right) \\ 2(-2x+3y-7z=1) \\ -4x+6y-7z=2\left(5\right) \end{gathered}$$

And on adding both the equations we get

$6x-6y+9z=18-4x+6y-14z=22x-5z=20$

Hence $2x-5z=20$

But in previous stem we got $2x-5z=1$

Hence the system is inconsistent

Conclusion

The system of equation is inconsistent