Question

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

$$\begin{gathered} x-y=6 \\ 2x-3z=16 \\ 2y+z=4 \end{gathered}$$

Short answer

The solution of the equation is$$\begin{gathered} x=8 \\ y=2 \\ z=0 \end{gathered}$$

Step-by-step solution

Given information

We are given

$$\begin{gathered} x-y=6 \\ 2x-3z=16 \\ 2y+z=4 \end{gathered}$$

Now multiply equation 1 by 2 and subtract from equation 3

We get,

$2x-2y=12$

Now we add this in equation 3 we get,

$2x-2y=12+2y+z=42x+z=16$

Now we subtract equation from 2, 

We get,

$2x+z=16-2x+3z=164z=0$

Hence$z=0$

Now substitute the value of z to find the value of x and y

We get,

$$\begin{gathered} 2x-3z=16 \\ 2x=16 \\ x=8 \end{gathered}$$

Now we find the values of y

$$\begin{gathered} 2y+z=4 \\ 2y=4 \\ y=2 \end{gathered}$$

Conclusion

The solution of system of equation is

$$\begin{gathered} x=8 \\ y=2 \\ z=0 \end{gathered}$$