Question

Write the system of linear equations represented by the augmented matrix. (Use variables x, y, and z, if applicable.)1 - 1 21-30 1 -1 50 0 1-5Use back-substitution to solve the system.(x, y, z) =

Answer 1

The augmented matrix represents the following system of linear equations:

$\begin{gathered} x-y+2z=-3 \\ y-z=5 \\ z=-5 \end{gathered}$

Use back substitution. It means, use the value of z given in the last equation, to find y in the second equation, and then, use these values to find x in the first equation:

$\begin{gathered} y-z=5 \\ y-(-5)=5 \\ y+5=5 \\ y=5-5 \\ y=0 \end{gathered}$$\begin{gathered} x-y+2z=-3 \\ x-0+2(-5)=-3 \\ x-10=-3 \\ x=-3+10 \\ x=7 \end{gathered}$

The solution of the system is (x, y, z)=(7, 0, -5)