The system of the linear equations is given by

x-y+5z=26...(1)

y+2z=1...(2)

z=6...(3)

To evaluate : The solution of the system of the linear equations

Step 2

Substitute the value of z from equation (3) into equation (2) we get,

\(\displaystyle{y}+{2}\times{6}={1}\)

\(\displaystyle\Rightarrow{y}+{12}={1}\)

\(\displaystyle\Rightarrow{y}=-{11}\)

Now, substitute the values of y and z in equation (1) we get,

\(\displaystyle{x}-{\left(-{11}\right)}+{5}\times{6}={26}\)

\(\displaystyle\Rightarrow{x}+{11}+{30}={26}\)

\(\displaystyle\Rightarrow{x}+{41}={26}\)

\(\displaystyle\Rightarrow{x}={26}-{41}\)

\(\displaystyle\Rightarrow{x}=-{15}\)

Hence, the solution of the stem of the linear equations is (x,y,z)=(-15,-11,6)