# Use back-substitution to solve the system of linear equations.\begin{cases}x &-y &+5z&=26\\ &\ \ \ y &+2z &=1 \\ & &\ \ \ \ \ z & =6\end{cases}(x,y,z)=()

Equations

Use back-substitution to solve the system of linear equations.
$$\begin{cases}x &-y &+5z&=26\\ &\ \ \ y &+2z &=1 \\ & &\ \ \ \ \ z & =6\end{cases}$$
(x,y,z)=()

2021-03-17
Step 1
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)